a second wronskian formulation of the boussinesq equation a wronskian formulation leading to rational solutions is presented for the boussinesq equation it involves third order linear partial differential equations whose representative systems are systematically solved the resulting solutions formulas provide a direct but powerful approach for constructing rational solutions positon solutions and complexiton solutions to the boussinesq equation various examples of exact solutions of those three kinds are computed the newly presented wronskian formulation is different from the one previously presented by li et al which does not yield rational solutions

complexiton and resonant multiple wave solutions to the 2 1 dimensional konopelchenko dubrovsky equation abstract in this paper the 2 1 dimensional konopelchenko dubrovsky kd equation is investigated using the hirota direct method and linear superposition principle the complexiton and resonant multiple wave solutions are successfully constructed for the hirota direct method it is essential that finding the bilinear form to the kd equation and applying its 2 n soliton formulation in real field to build the n complexiton solutions under the action of pairs of conjugate wave variables the linear superposition in real field of exponential traveling waves can generate the resonant multiple wave solutions and then generalize linear superposition principle to complex field we obtain some new resonant multiple wave type solutions the phenomena of complexiton resonant multiple wave and new resonant multiple wave type solutions are presented by figures

stability and isolation phenomena for yang mills fields in this article a series of results concerning yang mills fields over the euclidean sphere and other locally homogeneous spaces are proved using differential geometric methods one of our main results is to prove that any weakly stable yang mills field overs4 with groupg su2 su3 oru2 is either self dual or anti self dual the analogous statement for so4 bundles is also proved the other main series of results concerns gap phenomena for yang mills fields as a consequence of the non linearity of the yang mills equations we can give explicitc0 neighbourhoods of the minimal yang mills fields which contain no other yang mills fields in this part of the study the nature of the groupg does not matter neither is the dimension of the base manifold constrained to be four

multi soliton and double wronskian solutions of a 2 1 dimensional modified heisenberg ferromagnetic system a 2 1 dimensional modified heisenberg ferromagnetic system which arises in the motion of magnetization vector of the isotropic ferromagnet and biological pattern formation is investigated via the hirota bilinear method multi soliton solutions of such a system are derived it is proved that the system possesses the n soliton solutions expressed in terms of the double wronskian determinant head on and overtaking elastic interactions are exhibited elastic interaction behavior between the two solitons has been interpreted through the asymptotic analysis namely amplitude and velocity of each soliton remain unchanged except for the phase shift after the interaction inelastic interactions including the soliton fusion and fission between two solitons are shown during the soliton propagation for the product of two fields the soliton with the smaller amplitude can travel faster than with the larger while for the third field the soliton with the larger amplitude can travel faster than with the smaller on the other hand the soliton for the third field may exhibit the solitoff like property with respect to the three solitons head on elastic interaction can be found

periodic wave solutions of the boussinesq equation the boussinesq equation usually arises in a physical problem as a long wave equation the present work extends the search of periodic wave solutions for it the hirota bilinear method and riemann theta function are employed in the process we also analyse the asymptotic property of periodic waves in detail furthermore it is of interest to note that well known soliton solutions can be reduced from the periodic wave solutions

a study on resonant multi soliton solutions to the 2 1 dimensional hirota satsuma ito equations via the linear superposition principle abstract in this paper the existence and non existence of resonant multi soliton solutions to two different 2 1 dimensional hirota satsuma ito hsi equations are explored after applying the linear superposition principle we generate resonant multi soliton solutions to the first hsi equation which appeared in the theory of shallow water wave the conditions of real resonant multi soliton solutions are revealed the presented resonant multi soliton solutions exhibit the inelastic collision phenomenon among the involved solitary waves particularly upon choosing appropriate parameters we demonstrate the characteristics of inelastic interactions among the multi front kink waves both graphically and theoretically moreover non existence of resonant multi soliton solution is considered for the generalized hsi equation via the linear superposition principle

some new periodic solitary wave solutions of 3 1 dimensional generalized shallow water wave equation by lie symmetry approach abstract many important physical situations such as fluid flows marine environment solid state physics and plasma physics have been represented by shallow water wave equations in this article we construct new solitary wave solutions for the 3 1 dimensional generalized shallow water wave gsww equation by using optimal system of lie symmetry vectors the governing equation admits twelve lie dimension space a variety of analytic closed form solutions such as new periodic solitary wave cross kink soliton and doubly periodic breather type solutions have been obtained by using invariance of the concerned 3 1 dimensional gsww equation under one parameter lie group of transformations lie symmetry transformations have applied to generate the different forms of invariant solutions of the 3 1 dimensional gsww equation for different lie algebra lie symmetry method reduces 3 1 dimensional gsww equation into various ordinary differential equations odes while one of the lie algebra it is transformed into the well known 2 1 dimensional blmp equation it is affirmed that the proposed techniques are convenient genuine and powerful tools to find the exact solutions of nonlinear partial differential equations pdes under the suitable choices of arbitrary functions and parameters 2d 3d and contour graphics to the obtained results of gsww equation are also analyzed

two symmetry constraints for a generalized dirac integrable hierarchy abstract by a two by two matrix spectral problem a generalized dirac integrable hierarchy is presented a hamiltonian structure of the obtained hierarchy is established by trace identity and its liouville integrability is proved then through bargmann symmetry constraint spatial part of the lax pairs and adjoint lax pairs is nonlinearized as a completely integrable finite dimensional hamiltonian system next under an implicit symmetry constraint both spatial part and temporal parts of the lax pairs and adjoint lax pairs are all nonlinearized as completely integrable finite dimensional hamiltonian systems ultimately the involutive representation of solution of the generalized dirac integrable hierarchy is given

conformal fields and stability lagrangiens naturels conformes deformations conformes theoremes d instabilite pour des spheres theoremes d annulation sur des espaces non compacts

a direct method for minimizing the yang mills functional over 4 manifolds a direct method is employed to minimize the yang mills functional over a 4 dimensional manifold the limiting connection is shown to be yang mills but in a possibly new bundle we show that a topological invariant of the bundle is preserved by the minimizing process this implies the existence of an absolute minimum of the yang mills functional in a wide class of bundles

resonant behavior of multiple wave solutions to a hirota bilinear equation abstract for the exponential traveling wave solutions to the hirota bilinear equations a sufficient and necessary criterion for the existence of linear superposition principle has been given motivated by this criterion we propose a new hirota bilinear equation via using a multivariate polynomial applying the linear superposition principle to this new hirota bilinear equation we finally find two types of resonant multiple wave solutions among which the resonant three wave solutions are illustrated with three dimensional plots

rogue wave and a pair of resonance stripe solitons to kp equation abstract the rogue wave and a pair of resonance stripe solitons to kp equation are discovered first based on the bilinear method some lump solutions are obtained containing six parameters four of which must cater to the non zero conditions so as to insure the solution analytic and rationally localized second a one stripe soliton lump solution is presented and the interaction shows that the lump soliton can be drowned or swallowed by the stripe soliton conversely the lump soliton is spit out from the stripe soliton finally a new ansatz of combination of positive quadratic functions and hyperbolic functions is introduced and thus a novel nonlinear phenomenon is explored it is interesting that a rogue wave can be excited it is observed that the rogue wave possessing a peak wave profile arises from one of the resonance stripe solitons moves to the other and then disappears therefore a rogue wave can be generated by the interaction between the lump soliton and the pair of resonance stripe solitons however compared with classic rouge wave the dynamics of above nonlinear waves are quite different which are graphically demonstrated

statistical tests for presence of cyclostationarity the presence of kth order cyclostationarity is defined in terms of nonvanishing cyclic cumulants or polyspectra relying upon the asymptotic normality and consistency of kth order cyclic statistics asymptotically optimal spl chi sup 2 tests are developed to detect the presence of cycles in the kth order cyclic cumulants or polyspectra without assuming any specific distribution on the data constant false alarm rate tests are derived in both time and frequency domain and yield consistent estimates of possible cycles present in the kth order cyclic statistics explicit algorithms for k spl les 4 are discussed existing approaches are rather empirical and deal only with k spl les 2 case simulation results are presented to confirm the performance of the given tests

backlund transformation and solutions of a 3 1 dimensional nonlinear evolution equation in this paper bell polynomial method is used to study the integrability of a 3 1 dimensional nonlinear evolution equation we get the bilinear representation and backlund transformation of the equation the exact solutions are obtained by means of linear superposition principle and homoclinic test approach

two integrable lattice hierarchies and their respective darboux transformations two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived and the infinitely many conservation laws of the first integrable model is obtained moreover the darboux transformations based on different darboux matrixes 2 3 4 and 3 2 4 for the above mentioned integrable hierarchies are established with the help of two different gauge transformations of lax pairs in this paper as an application the explicit solutions of the two integrable hierarchies are presented

2 1 dimensional rossby waves with complete coriolis force and its solution by homotopy perturbation method abstract in this paper the effects of both complete coriolis force and dissipation on equatorial nonlinear rossby wave are investigated analytically from the quasi geostrophic potential vorticity equation by using methods of multiple scales and perturbation expansions a 2 1 dimensional nonlinear zakharov kuznetsov burgers equation is derived in describing the evolution of rossby wave amplitude the effects of generalized beta the horizontal component of coriolis parameter and the dissipation are presented from the zakharov kuznetsov burgers equation we also obtain the classical solitary solution of the zakharov kuznetsov equation when the dissipation is absent by elliptic function expansion method and the complete coriolis force effect can be seen by the solution but the method is failed to zakharov kuznetsov burgers equation therefore we use the efficient homotopy perturbation method to solve the zakharov kuznetsov burgers equation

small coupling limit and multiple solutions to the dirichlet problem for yang mills connections in four dimensions ii in this paper we complete the proof of the existence of multiple solutions and in particular non minimal ones to the e dirichlet problem obtained as a variational problem for the su 2 e yang mills functional this is equivalent to proving the existence of multiple solutions to the dirichlet problem for the su 2 yang mills functional with small boundary data in the first paper of this series this non compact variational problem is transformed into the finite dimensional problem of finding the critical points of the function je q which is essentially the yang mills functional evaluated on the approximate solutions constructed via a gluing technique in the present paper we establish a morse theory for je q by means of ljusternik schnirelmann theory thus complete the proofs of theorems 1 3 given by isobe and marini small coupling limit and multiple solutions to the dirichlet problem for yang mills connections in 4 dimensions part i j math phys 53 063706 2012 10 1063 1 4728211

construction of new exact rational form non travelling wave solutions to the 2 1 dimensional generalized broer kaup system abstract with the aid of symbolic computation maple several new families of rational form variable separation solutions with three arbitrary functions to the 2 1 dimensional generalized broer kaup system are derived by using an improved mapping approach and a variable separation approach these solutions include rational solitary wave solutions periodic wave solutions and rational wave solutions the properties of the novel localized excitation are revealed by some figures

the classification of the single traveling wave solutions to the generalized equal width equation abstract the complete discrimination system for polynomial is applied to the generalized equal width ew equation to obtain the classifications of single traveling wave solutions in particular we construct the corresponding solutions for the concrete parameters to show that each solution in the classification can be realized

multiple soliton solutions and fusion interaction phenomena for the 2 1 dimensional modified dispersive water wave system by means of backlund transformation and the hirota bilinear method the 2 1 dimensional modified dispersive water wave system is investigated with the aid of symbolic computation new multiple soliton solutions with arbitrary functions are derived based on the derived solutions rich coherent structures like dromions peakons and compactons can be derived and moreover the fusion interactions among different types of localized structures are graphically studied which might be helpful to understand the propagation processes for nonlinear and dispersive long gravity waves on shallow waters

bifrequency and bispectrum maps a new look at multirate systems with stochastic inputs in multirate digital signal processing we often encounter decimators interpolators and complicated interconnections of these with lti filters we also encounter cyclo wide sense stationary cwss processes and linear periodically time varying ptv systems it is often necessary to understand the effects of multirate systems on the statistical properties of their input signals some of these issues have been addressed earlier for example it has been shown that a necessary and sufficient addition for the output of an l fold interpolation filter to be wide sense stationary wss for all wss inputs is that the filter was an alias free l support however several questions of this nature remain unanswered for example what is the necessary and sufficient condition on a pair or more generally a bank of interpolation filters so that their outputs are jointly wss jwss for all jointly wss inputs what is the condition if only the sum of their outputs is required to be wss when is the output of an lptv system for example a uniform filter bank wss for all wss inputs some of these questions may appear to be simple generalizations of the above mentioned result for a single interpolation filter however the frequency domain approaches that proved this result are quite difficult to generalize to answer these questions the purpose of this paper is to provide these answers using analysis based on bifrequency maps and bispectra these tools are two dimensional 2 d fourier transforms that characterize linear time varying ltv systems and nonstationary random processes respectively we show that the questions raised above are addressed elegantly and in a geometrically insightful way using these tools we also derive a bifrequency characterization lossless ltv systems this may potentially lead to an increased understanding of these systems

convergence of yang mills higgs fields in this paper we study the convergence of yang mills higgs ymh fields defined on fiber bundles over riemann surfaces where the fiber is a compact symplectic manifold and the conformal structure of the underlying surface is allowed to vary we show that away from the nodes the ymh fields converges up to gauge to a smooth ymh field modulo finitely many harmonic spheres while near the nodes where the conformal structure degenerates the ymh fields converges to a pair consisting of a flat connection and a twisted geodesic with potential in particular we generalize the recent compactness results on both harmonic maps from surfaces and twisted holomorphic curves to general ymh fields

variable separation solutions to the coupled integrable dispersionless equations abstract in this paper the variable separation solutions of the coupled integrable dispersionless equations are derived these solutions include two arbitrary functions and they are more general than the results presented before furthermore some coherent structures of the physical quantity including decaying bell solitary single dromion soliton type breather peakon type breather and loop type breather are constructed

sampling of spectrally correlated processes the problem of sampling continuous time spectrally correlated sc processes is addressed sc processes have loeve bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane this class of nonstationary processes extends that of the almost cyclostationary processes and occurs in wideband mobile communications and spectral analysis with nonuniform spectral resolution the class of the discrete time sc processes is introduced and characterized it is shown that such processes can be obtained by uniformly sampling the continuous time sc processes sampling theorems are presented and sufficient conditions to avoid aliasing are provided applications are illustrated with reference to the problem of cross spectral analysis with nonuniform frequency resolution and the propagation of communications signals through mimo multipath doppler channels

exact wave solutions for a 3 1 dimensional generalized b type kadomtsev petviashvili equation abstract in this work we investigate a 3 1 dimensional generalized b type kadomtsev petviashvili equation based on the simplified hirota bilinear method we first construct its soliton solutions meanwhile we correct the formula of n soliton solution for this equation on the basis of these solitons we further calculate its lump solutions periodic waves meanwhile rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method some figures are given to display the behavior of these solutions

yang mills fields which are not self dual the purpose of this paper is to prove the existence of a new family of non self dual finite energy solutions to the yang mills equations on euclidean four space withsu 2 as a gauge group the approach is that of equivariant geometry attention is restricted to a special class of fields those that satisfy a certain kind of rotational symmetry for which it is proved that 1 a solution to the yang mills equations exists among them and 2 no solution to the self duality equations exists among them the first assertion is proved by an application of the direct method of the calculus of variations existence and regularity of minimizers and the second assertion by studying the symmetry properties of the linearized self duality equations the same technique yields a new family of non self dual solutions on the complex projective plane

quasi periodic waves and an asymptotic property for the asymmetrical nizhnik novikov veselov equation based on a multi dimensional riemann theta function the hirota bilinear method is extended to explicitly construct multi periodic quasi periodic wave solutions for the asymmetrical nizhnik novikov veselov equation among these periodic waves two periodic waves are a direct generalization of well known cnoidal waves their surface pattern is two dimensional the main physical result is the description of the behavior of nonlinear waves in shallow water a limiting procedure is presented to analyze asymptotic properties of the two periodic waves in details relations between the periodic wave solutions and the well known soliton solutions are established it is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit

diversity of interaction solutions to the 2 1 dimensional ito equation abstract we aim to show the diversity of interaction solutions to the 2 1 dimensional ito equation based on its hirota bilinear form the proof is given through maple symbolic computations an interesting characteristic in the resulting interaction solutions is the involvement of an arbitrary function special cases lead to lump solutions lump soliton solutions and lump kink solutions two illustrative examples of the resulting solutions are displayed by three dimensional plots and contour plots

grammian type determinant solutions to generalized kp and bkp equations abstract grammian type determinant identities of the bilinear kp hierarchy and a useful property on the derivatives of grammians are proposed based on these grammian type determinant identities three grammian structures are furnished to a large class of generalized nonlinear kp and bkp type equations all the generating functions for matrix entries satisfy a system of combined linear partial differential equations in the first case of the class of generalized kp and bkp equations general rational solutions are given making use of its grammian formulation

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

multirate processing of time series exhibiting higher order cyclostationarity the paper investigates the effects of multirate systems on the higher order wide sense cyclostationarity wscs properties of discrete time series to this end definitions and properties of the cyclic higher order statistics which were introduced for continuous time series in the fraction of time probability framework are first extended to discrete time series then starting from the consideration of the basic multirate building blocks viz m fold decimators and l fold interpolators results for typical interconnections are derived the problem of eliminating the images in the cyclic higher order spectra of an interpolated time series is addressed moreover the problem of avoiding aliasing in both cycle and spectral frequency domains in the cyclic higher order spectra of a decimated time series is considered finally a sufficient condition to avoid both aliasing and imaging effects in the cyclic higher order spectra of a time series decimated by a fractional factor is derived

the classification and representation of single traveling wave solutions to the generalized fornberg whitham equation abstract by the complete discrimination system for polynomial method we give the classification and representation of single traveling wave solutions to the generalized fornberg whitham equation with n 1 and n 2

path connected yang mills moduli spaces on utilise des techniques de min max dans le calcul des variations pour demontrer que les espaces modules des connexions auto duales sur des fibres principaux su 2 ou su 3 sur s 4 sont chemin connexe

a framework for morse theory for the yang mills functional on explique comment la theorie de morse pour la fonctionnelle de yang mills peut se retrouver en examinant la restriction de la fonctionnelle a un ensemble denombrable de varietes non compactes de dimension finie

asymptotic theory of mixed time averages and kth order cyclic moment and cumulant statistics we generalize parzen s 1961 analysis of asymptotically stationary processes to mixtures of deterministic stationary nonstationary and generally complex time series under certain mixing conditions expressed in terms of joint cumulant summability we show that time averages of such mixtures converge in the mean square sense to their ensemble averages we additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions these conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes as an important consequence we develop consistent and asymptotically normal estimators for time varying and cyclic moments and cumulants of kth order cyclostationary processes and provide computable variance expressions some examples are considered to illustrate the salient features of the analysis

localized waves and interaction solutions to a 3 1 dimensional generalized kp equation abstract based on the hirota bilinear method and long wave limit four kinds of localized waves namely solitons lumps breathers and rogue waves are constructed for the 3 1 dimensional generalized kp equation n soliton solutions are obtained by employing bilinear method then breathers two breathers and interaction breather solutions are obtained by selecting appropriate parameters on two soliton solution and four soliton solution these breathers own different dynamic behaviors in the different planes taking a long wave limit on the two and four soliton solutions under special parameter constraints one order lumps and rogue waves two order lumps and rogue waves and interaction solutions between lumps and rogue waves are derived applying the same method on the three soliton solution interaction solutions between kink solitons with periodic solutions lumps and rogue waves are constructed respectively the influence of parameters on the solution is analyzed the propagation directions phase shifts energies and shapes for these solutions can be affected and controlled by the parameters moreover graphics are presented to demonstrate the properties of the explicit analytical localized wave solutions

soliton solution to bkp equation in wronskian form we find out a group of identities named wronskian identities of bilinear kp hierarchy here as well as two useful properties of d operator this makes it possible to easily search for some new wronskian solutions for pde which owns bilinear form and to simplify the process of the proof as an application of this new method we propose the first wronskian condition for the bkp i equation and for the bkp ii equation respectively in addition we also discuss several generalized bkp equations and obtain their wronskian conditions

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

hirota bilinear equations with linear subspaces of hyperbolic and trigonometric function solutions linear superposition principles of hyperbolic and trigonometric function solutions are analyzed for hirota bilinear equations with an aim to construct a specific sub class of n soliton solutions formulated by linear combinations of hyperbolic and trigonometric functions an algorithm using weights is discussed and a few illustrative application examples are presented

resonant soliton and complexiton solutions for 3 1 dimensional boiti leon manna pempinelli equation abstract in this letter the linear superposition principle is used to discuss the 3 1 dimensional boiti leon manna pempinelli equation with bilinear derivatives as a result we obtain new resonant soliton and complexiton solutions by discussing two different cases involved the parameters these solutions are a class of n wave solutions of linear combinations of exponential traveling waves

nonparametric polyspectral estimators for kth order almost cyclostationary processes second and higher order almost cyclostationary processes are random signals with almost periodically time varying statistics the class includes stationary and cyclostationary processes as well as many real life signals of interest cyclic and time varying cumulants and polyspectra are defined for discrete time real kth order cyclostationary processes and their interrelationships are explored smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal asymptotic covariance expressions are derived along with their computable forms higher than second order cyclic cumulants and polyspectra convey time varying phase information and are theoretically insensitive to any stationary for nonzero cycles as well as additive cyclostationary gaussian noise for all cycles

symmetric instantons and the adhm construction we construct allsu 2 yang mills instantons ons 4 that admit a certain symmetry quadrupole symmetry this is accomplished by an equivariant version of the adhm monad classification of instantons this work is part of an attempt to better understand the structure of non self dual yang mills connections with the same symmetry

non self dual yang mills connections with quadrupole symmetry we prove the existence of non self dual yang mills connections onsu 2 bundles over the four sphere specifically on all bundles with second chern number not equal 1 we study connections equivariant under ansu 2 symmetry group to reduce the effective dimensionality from four to one and then use variational techniques the existence of non self dualsu 2 ym connections on the trivial bundle second chern number equals zero has already been established by sibner sibner and uhlenbeck via different methods

applications of linear superposition principle to resonant solitons and complexitons we apply the linear superposition principle to hirota bilinear equations and generalized bilinear equations by extending the linear superposition principle to complex field we construct complex exponential wave function solutions first and then get complexions by taking pairs of conjugate parameters a few examples of mixed resonant solitons and complexitons to hirota and generalized bilinear differential equations are presented

double sub equation method for complexiton solutions of nonlinear partial differential equations a double sub equation method is presented for constructing complexiton solutions of nonlinear partial differential equations pdes the main idea of the method is to take full advantage of two solvable ordinary differential equations with different independent variables with the aid of maple one can obtain both complexiton solutions combining elementary functions and the jacobi elliptic function solutions to nonlinear pdes some illustrative equations are investigated by this means and the corresponding complexiton solutions are computed

generalized wronskian solutions for the 3 1 dimensional jimbo miwa equation abstract more general wronskian conditions are constructed for the 3 1 dimensional jimbo miwa equation as a result the generalized wronskian solutions including rational solutions positons negatons solitons and interaction solutions are obtained moreover some new solutions together with some known solutions given by other solving methods are derived from these wronskian solutions

solutions to yang mills equations that are not self dual abstract the yang mills functional for connections on principle su 2 bundles over s4 is studied critical points of the functional satisfy a system of second order partial differential equations the yang mills equations if in particular the critical point is a minimum it satisfies a first order system the self dual or anti self dual equations here we exhibit an infinite number of finite action nonminimal unstable critical points they are obtained by constructing a topologically nontrivial loop of connections to which min max theory is applied the construction exploits the fundamental relationship between certain invariant instantons on s4 and magnetic monopoles on h3 this result settles a question in gauge field theory that has been open for many years

multiple soliton solutions for the generalized 1 1 dimensional and the generalized 2 1 dimensional ito equations abstract the generalized 1 1 dimensional and the generalized 2 1 dimensional ito equations obtained by introducing a new type of bilinearism are studied the tanh coth method is used to obtain single soliton solutions and periodic solutions for the ito equations the hirota bilinear method is used to determine the multiple soliton solutions of sech squared type for these equations new entirely solutions are obtained the analysis emphasizes the power of the two methods and its capability of handling completely integrable equations

dressing method for the vector sine gordon equation and its soliton interactions in this paper we develop the dressing method to study the exact solutions for the vector sine gordon equation the explicit formulas for one kink and one breather are derived the method can be used to construct multi soliton solutions two soliton interactions are also studied the formulas for position shift of the kink and position and phase shifts of the breather are given these quantities only depend on the pole positions of the dressing matrices

time fractional generalized boussinesq equation for rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions abstract construct fractional order model to describe rossby solitary waves can provide more pronounced effects and deeper insight for comprehending generalization and evolution of rossby solitary waves in stratified fluid in the paper from the quasi geostrophic vorticity equation with dissipation effect and complete coriolis force based on the multi scale analysis and perturbation method a classical generalized boussinesq equation is derived to describe the rossby solitary waves in stratified fluid further by employing the reduction perturbation method the semi inverse method the agrawal method we derive the euler lagrangian equation of classical generalized boussinesq equation and obtain the time fractional generalized boussinesq equation without dissipation effect by using lie group analysis method the conservation laws of time fractional boussinesq equation are given finally with the help of the improved g g expansion method the exact solutions of the above equation are generated meanwhile in order to consider the dissipation effect we have to derive the approximate solutions by adopting the new iterative method we remark that the fractional order model can open up a new window for better understanding the waves in fluid

lump solutions to the kadomtsev petviashvili i equation with a self consistent source abstract based on symbolic computations lump solutions to the kadomtsev petviashvili i kpi equation with a self consistent source kpiescs are constructed by using the hirota bilinear method and an ansatz technique in contrast with lower order lump solutions of the kadomtsev petviashvili kp equation the presented lump solutions to the kpiescs exhibit more diverse nonlinear phenomena the method used here is more natural and simpler

heat flow of yang mills higgs functionals in dimension two abstract we consider the heat flow of yang mills higgs functional where the base manifold is a riemannian surface and the fiber is a compact symplectic manifold we show that the corresponding cauchy problem admits a global weak solution for any h 1 initial data moreover the solution is smooth except for finitely many singularities we prove an energy identity at finite time singularities and give a description of the asymptotic behavior at time infinity

novel interaction phenomena of localized waves in the generalized 3 1 dimensional kp equation abstract based on hirota bilinear method the n soliton solution of the 3 1 dimensional generalized kadomtsev petviashvili equation is derived explicitly from which some localized waves such as soliton breather lump and their interactions are obtained by the approach of long wave limit especially by selecting particular parameter constraints in the n soliton solutions the one breather or one lump can be obtained from two soliton the elastic interaction solutions between one bell shaped soliton and one breather or between one bell shaped soliton and one lump can be obtained from three soliton the elastic interaction solutions among two bell shaped solitons and one breather among two bell shaped solitons and one lump between two breathers or between two lumps can be obtained from four soliton the elastic interactions solutions among one bell shaped soliton and two breathers among one breather and three bell shaped solitons among one lump and three bell shaped solitons among one bell shaped soliton and two breathers or among one breather one lump and one bell shaped soliton can be obtained from five soliton detailed behaviors of such interaction phenomena are illustrated analytically and graphically the results obtained in this paper may be helpful for understanding the evolution of nonlinear localized waves in shallow water

hirota bilinear equations with linear subspaces of solutions we explore when hirota bilinear equations possess linear subspaces of solutions first we establish a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions to hirota bilinear equations second we show that multivariate polynomials whose zeros form a vector space can generate the desired hirota bilinear equations with given linear subspaces of solutions and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero third applying an algorithm using weights we present parameterizations of wave numbers and frequencies achieved by using one parameter to compute the desired hirota bilinear equations

extended wave solutions for a nonlinear klein gordon zakharov system abstract the nonlinear klein gordon zakharov kgz system is used as a vehicle to employ the sine cosine method and the extended tanh method to construct formally exact wave solutions each method presents various solutions with distinct formal properties and physical structures which mainly include new periodic wave solutions traveling wave solutions and solitary solutions in addition as special cases some of new rational functions type solutions are developed and extended

median based cyclic polyspectrum estimation in this paper median based estimation methods for the cyclic polyspectrum are proposed the algorithms do not require a priori knowledge of the spl beta submanifolds that is they do not require the knowledge of all of the lower order cycle frequencies of the time series available for the estimation of the cyclic polyspectrum therefore such methods are particularly useful when the cyclostationarity of the signals under consideration is not completely known the proposed estimators converge to the theoretical values of the cyclic polyspectrum when the collect time approaches infinity and the spectral resolution becomes infinitesimal furthermore their accuracy is very nearly the same as that of the usual time and frequency smoothed cyclic periodogram methods that use a priori knowledge of lower order cycle frequencies to avoid the spl beta submanifolds

gauge theories on four dimensional riemannian manifolds this paper develops the riemannian geometry of classical gauge theories yang mills fields coupled with scalar and spinor fields on compact four dimensional manifolds some important properties of these fields are derived from elliptic theory regularity an energy gap theorem the manifold structure of the configuration space and a bound for the supremum of the field in terms of the energy it is then shown that finite energy solutions of the coupled field equations cannot have isolated singularities this extends a theorem of k uhlenbeck

linear time variant transformations of generalized almost cyclostationary signals i theory and method the problem of linear time variant filtering is addressed in the fraction of time fot probability framework the adopted approach which is an alternative to the classical stochastic one provides a statistical characterization of the system in terms of time averages of functions of time rather than ensemble averages of stochastic processes thus it is particularly useful when stochastic systems transform ergodic input signals into nonergodic output signals as it happens with several channel models encountered in practice the analysis is carried out with reference to the wide class of the generalized almost cyclostationary signals which includes as a special case the class of almost cyclostationary signals in this paper systems are classified as deterministic or random in the fot probability framework moreover the new concept of expectation in the fot probability framework of the impulse response function of a system is introduced for the linear time variant systems the higher order system characterization in the time domain is provided in terms of the system temporal moment function which is the kernel of the operator that transforms the additive sinewave components contained in the input lag product into the additive sinewave components contained in the output lag product moreover the higher order characterization in the frequency domain is also provided and input output relationships are derived in terms of temporal and spectral moment and cumulant functions developments and examples of application of the theory introduced here are presented in part ii of this two part paper

the n soliton solution and localized wave interaction solutions of the 2 1 dimensional generalized hirota satsuma ito equation abstract in this paper the n soliton solution is constructed for the 2 1 dimensional generalized hirota satsuma ito equation from which some localized waves such as line solitons lumps periodic solitons and their interactions are obtained by choosing special parameters especially by selecting appropriate parameters on the multi soliton solutions the two soliton can reduce to a periodic soliton or a lump soliton the three soliton can reduce to the elastic interaction solution between a line soliton and a periodic soliton or the elastic interaction between a line soliton and a lump soliton while the four soliton can reduce to elastic interaction solutions among two line solitons and a periodic soliton or the elastic interaction ones between two periodic solitons detailed behaviours of such solutions are illustrated analytically and graphically by analysing the influence of parameters finally an inelastic interaction solution between a lump soliton and a line soliton is constructed via the ansatz method and the relevant interaction and propagation characteristics are discussed graphically the results obtained in this paper may be helpful for understanding the interaction phenomena of localized nonlinear waves in two dimensional nonlinear wave equations

a deformed reduced semi discrete kaup newell equation the related integrable family and darboux transformation we propose a deformed reduced semi discrete kaup newell equation we derive the related integrable family through discrete zero curvature equation we establish a darboux transformation of lax pair of the proposed equation three exact solutions are given a deformed reduced semi discrete kaup newell equation and its related integrable family are derived from discrete zero curvature equation a darboux transformation of lax pair of this equation is established with the help of gauge transformation by means of the resulting darboux transformation three exact solutions are given

resonant multiple wave solutions for a 3 1 dimensional nonlinear evolution equation by linear superposition principle the linear superposition principle can apply to the construction of resonant multiple wave solutions for a 3 1 dimensional nonlinear evolution equation two types of resonant solutions are obtained by the parameterization for wave numbers and frequencies for linear combinations of exponential traveling waves the resonance phenomena of multiple waves are discussed through the figures for several sample solutions

nonlocal symmetry darboux transformation and soliton cnoidal wave interaction solution for the shallow water wave equation abstract in classical shallow water wave sww theory there exist two integrable one dimensional sww equation hirota satsuma hs type and ablowitz kaup newell segur akns type in the boussinesq approximation in this paper we mainly focus on the integrable sww equation of akns type the nonlocal symmetry in form of square spectral function is derived starting from its lax pair infinitely many nonlocal symmetries are presented by introducing the arbitrary spectrum parameter these nonlocal symmetries can be localized and the sww equation is extended to enlarged system with auxiliary dependent variables then darboux transformation for the prolonged system is found by solving the initial value problem similarity reductions related to the nonlocal symmetry and explicit group invariant solutions are obtained it is shown that the soliton cnoidal wave interaction solution which represents soliton lying on a cnoidal periodic wave background can be obtained analytically interesting characteristics of the interaction solution between soliton and cnoidal periodic wave are displayed graphically

n solitons breathers lumps and rogue wave solutions to a 3 1 dimensional nonlinear evolution equation abstract based on hirota bilinear method n solitons breathers lumps and rogue waves as exact solutions of the 3 1 dimensional nonlinear evolution equation are obtained the impacts of the parameters on these solutions are analyzed the parameters can influence and control the phase shifts propagation directions shapes and energies for these solutions the single kink soliton solution and interactions of two and three kink soliton overtaking collisions of the hirota bilinear equation are investigated in different planes the breathers in three dimensions possess different dynamics in different planes via a long wave limit of breathers with indefinitely large periods rogue waves are obtained and localized in time it is shown that the rogue wave possess a growing and decaying line profile that arises from a nonconstant background and then retreat back to the same nonconstant background again the results can be used to illustrate the interactions of water waves in shallow water moreover figures are given out to show the properties of the explicit analytic solutions

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

pfaffian solutions to a 3 1 dimensional generalized b type kadomtsev petviashvili equation and its modified counterpart abstract a class of exact pfaffian solutions to a 3 1 dimensional generalized b type kadomtsev petviashvili equation is obtained a set of sufficient conditions consisting of systems of linear partial differential equations involving free parameters is generated to guarantee that the pfaffian solves the equation a backlund transformation of the equation is presented the equation is transformed into a set of bilinear equations and a few classes of traveling wave solutions rational solutions and pfaffian solutions to the extended bilinear equations are furnished examples of the pfaffian solutions are explicitly computed and a few solutions are plotted

lump solutions to a 2 1 dimensional extended kp equation abstract with the aid of a computer algebra system we present lump solutions to a 2 1 dimensional extended kadomtsev petviashvili equation ekp and give the sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions we plot a few solutions for some specific values of the free parameters involved and finally derive one of the lump solutions of the kadomtsev petviashvili kp equations from the lump solutions of the ekp equation

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

lump solutions of a generalized calogero bogoyavlenskii schiff equation abstract a generalized calogero bogoyavlenskii schiff equation is considered and based on its hirota bilinear form a class of lump solutions is explicitly generated via symbolic computations with maple together with plots of a specific lump solution the result enlarges the category of nonlinear partial differential equations which possess lump solutions

morse theory for the yang mills functional via equivariant homotopy theory in this paper we show the existence of non minimal critical points of the yang mills functional over a certain family of 4 manifolds m29 g 0 1 2 with generic su 2 invariant metrics using morse and homotopy theoretic methods these manifolds are acted on fixed point freely by the lie group su 2 with quotient a compact riemann surface of even genus we use a version of invariant morse theory for the yang mills functional used by parker in a morse theory for equivariant yang mills duke math j 66 2 1992 337 356 and rade in compactness theorems for invariant connections submitted for publication

an integrable hierarchy and darboux transformations bilinear backlund transformations of a reduced equation a new integrable hierarchy of evolution equations is obtained by making use of a lie algebra and tu ma scheme from which a new generalized broer kaup gbk equation is produced then two kinds of darboux transformations the bilinear presentation the bilinear backlund transformation and the new lax pair of the gbk equation are generated respectively by employing the bell polynomials

quasi periodic wave solution and asymptotic behavior for the 2 1 dimensional toda lattice equation abstract one and two periodic wave solutions for the 2 1 dimensional toda lattice equation are presented based on the hirota bilinear method and the riemann theta function the asymptotic behaviors of these two solutions are considered and the rigorous proof is given that the periodic wave solutions tend to the soliton solutions in an appropriate limiting procedure

diversity of exact solutions to a 3 1 dimensional nonlinear evolution equation and its reduction abstract in this paper a 3 1 dimensional nonlinear evolution equation and its reduction is studied by use of the hirota bilinear method and the test function method with symbolic computation diversity of exact solutions is obtained by solving the under determined nonlinear system of algebraic equations for the associated parameters finally analysis and graphical simulation are given to reveal the propagation and dynamical behavior of the solutions

linear superposition principle of hyperbolic and trigonometric function solutions to generalized bilinear equations linear subspaces of hyperbolic and trigonometric function solutions to generalized bilinear equations are analyzed necessary and sufficient conditions are presented to apply the linear superposition principles applications of an algorithm using weights are made together with a few concrete examples

complexiton solutions to soliton equations by the hirota method we apply the hirota direct method to construct complexiton solutions complexitons the key is to use hirota bilinear forms we prove that taking pairs of conjugate wave variables in the 2n soliton solutions generates n complexion solutions the general theory is used to construct multi complexion solutions to the korteweg de vries equation