the tanh and the sine cosine methods for the complex modified k dv and the generalized k dv equations the complex modified k dv cmk dv equation and the generalized k dv equation are investigated by using the tanh method and the sine cosine method a variety of exact travelling wave solutions with compact and noncompact structures are formally obtained for each equation the study reveals the power of the two schemes where each method complements the other

patterns on liquid surfaces cnoidal waves compactons and scaling abstract localized patterns and nonlinear oscillation formations on the bounded free surface of an ideal incompressible liquid are investigated cnoidal modes solitons and compactons as traveling non axially symmetric shapes are discussed a finite difference differential generalized korteweg de vries kdv equation is shown to describe the three dimensional motion of the fluid surface and in the limit of long and shallow channels one recovers the well known kdv equation a tentative expansion formula for the representation of the general solution of a nonlinear equation for given initial conditions is introduced the model is useful in multilayer fluid dynamics cluster formation and nuclear physics since up to an overall scale these systems display a free liquid surface behavior

convergence of the ssor method for nonlinear systems of simultaneous equations in der vorliegenden arbeit wird fur die konvergenz des symmetrischen relaxationsverfahrens ssor verfahren bei anwendung auf eine klassenichtlinearer gleichungssysteme die globale konvergenz bewiesen diese gleichungssysteme treten z b bei der diskretisierung nichtlinearer partieller differentialgleichungen auf

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

the effect of the order of nonlinear dispersive equation on the compact and noncompact solutions the effect of the order of nonlinear dispersive partial differential equation on the compact and noncompact solutions is studied in this paper two variants of the kdv equation of odd orders are examined our analysis reveals that the physical nature of these nonlinear kdv type of equations are different two distinct sets of general formulas for each type of variants are performed to present a fairly complete understanding of the compact and noncompact structures

optimal antenna currents for q superdirectivity and radiation patterns using convex optimization the high q factor low bandwidth and low efficiency make the design of small antennas challenging here convex optimization is used to determine current distributions that provide upper bounds on the antenna performance optimization formulations for maximal gain q factor quotient minimal q factor for superdirectivity and minimum q for given far fields are presented the effects of antennas embedded in structures are also discussed the results are illustrated for planar geometries

numerically induced phase shift in the kdv soliton abstract when using a finite difference scheme to study the motion of a kdv solition a shift in the position of the solition from the exact solution is detected in this paper we retain the lowest order terms in the truncation error and treat them analytically as a perturbation of the kdv equation it is found that perturbation theory can be used to determine the numerically induced shift

convergence of asynchronous iteration with arbitrary splitting form abstract the convergence theorem of asynchronous iteration for solving a system of linear equations presented by d chazan and w miranker is proved with a new method and generalized to splitting iteration with arbitrary form

generalization of exp function and other standard function methods exp function and other standard function methods for solving nonlinear differential equations are generalized in this paper an analytical criterion determining if a solution can be expressed in a form comprising standard functions is derived new computational algorithm for automatic identification of the structure of the solution is constructed the algorithm provides information if the solution can be expressed as a sum of standard functions a ratio of sums of standard functions or even a more complex algebraic form involving standard functions several examples are used to illustrate the proposed concept

a concept of nonlinear block diagonal dominance we introduce a concept of block diagonal dominance for nonlinear functions and discuss the relations to strictly diagonally dominant functions and m functions some sufficient conditions for the new kind of functions are given the global convergence of block asynchronous sor methods for finding zeros of block diagonal dominant nonlinear functions is proved

adiabatic perturbations for compactons under dissipation and numerically induced dissipation compacton propagation under dissipation shows amplitude damping and the generation of tails the numerical simulation of compactons by means of dissipative schemes also show the same behaviors the truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis for dissipative schemes or when artificial dissipation is added the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically induced tails in this paper such methods are applied to the k 2 2 rosenau hyman equation showing a very good agreement between perturbative and numerical results

field patterns of resonant noncircular closed loop arrays further analysis previous papers have introduced the continuous current model for resonant closed loop arrays of cylindrical dipoles and for a certain class of array shapes have determined the resulting field patterns analytically those analytical calculations involve several approximations in the present paper we first study the aforementioned model numerically for the case of elliptical closed loop arrays the results which involve fewer approximations than those of the previous papers but which refer to different array shapes imply that elliptical arrays have a bidirectional highly directive field and unlike conventional arrays have no sidelobes combining analytical and numerical methods we then investigate the relationship between the aforementioned continuous current model and what we call the discrete current model which in a certain sense is more realistic the results indicate that subject to suitable conditions the two models yield virtually identical results in our analytical investigations an important tool is the poisson summation formula for finite sums we have devoted a stand alone section to this formula which supplements recent unrelated publications in antenna theory

asynchronous parallel methods for enclosing solutions of nonlinear equations we consider interval arithmetic based parallel methods for enclosing solutions of nonlinear systems of equations where processors are allowed to proceed asynchronously we present a general study on the convergence of asynchronous iterations in interval spaces and apply them to a variety of methods for the nonlinear equations case the convergence results turn out to be very similar to those known for synchronous methods several practical examples on shared memory architectures are included the asynchronous methods sometimes perform substantially better than their synchronous counterparts

compactons and solitary patterns structures for variants of the kdv and the kp equations in this paper we discuss mathematical variants in higher dimensions of the kdv and the kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the study presents a fairly complete understanding of the compact and noncompact dispersive structures

on asynchronous iterations asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times this paper reviews certain models of asynchronous iterations using a common theoretical framework the corresponding convergence theory and various domains of applications are presented these include nonsingular linear systems nonlinear systems and initial value problems

exact travelling wave solutions for the generalized nonlinear schrodinger gnls equation with a source by extended tanh coth sine cosine and exp function methods the capability of extended tanh coth sine cosine and exp function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed in this study the generalized nonlinear schrodinger gnls equation is solved by three different methods to obtain the single soliton solutions for the equation the extended tanh coth and sine cosine methods are used furthermore for this nonlinear evolution equation the exp function method is applied to derive various travelling wave solution results show that while the first two procedures easily provide a concise solution the exp function method provides a powerful mathematical means for solving nonlinear evolution equations in mathematical physics

models of parallel chaotic iteration methods abstract we consider two models of parallel multisplitting chaotic iterations for solving large nonsingular systems of equations ax b in the first model each processor can carry out an arbitrary number of local iterations before the next global approximation to the solution is formed in the second model any processor can update the global approximation which resides in the central processor at any time this model is a generalization of a sequential iterative scheme due to ostrowski called the free steering group jacobi iterative scheme and a chaotic relaxation point iterative scheme due to chazan and miranker we show that when a is a monotone matrix and all the splittings are weak regular both models lead to convergent schemes

convergence of partially asynchronous block quasi newton methods for nonlinear systems of equations in this paper a partially asynchronous block broyden method is presented for solving nonlinear systems of equations of the form f x 0 sucient conditions that guarantee its local convergence are given in particular local convergence is shown when the jacobian f 0 x i s anh matrix where x is the zero point of f the results are extended to schubert s method a connection with discrete schwarz alternating procedure is also shown c 1999 elsevier science b v all rights reserved

surface wave and superdirectivity aspects of effective current for linear antennas previous papers have defined the concept of effective current for linear antennas as a method of postprocessing the unphysical solutions obtained by applying discretization galerkin methods to the usual integral equations that employ the approximate or reduced kernel such an unphysical solution can be thought of as an auxiliary rapidly oscillating current located on the axis of the linear antenna while the effective current is the magnetic field due to the oscillating current at a distance equal to the antenna radius multiplied by a factor equal to the antenna circumference in the present paper we focus on the rapid decrease of the aforementioned magnetic field and point out similarities to surface waves to the well known phenomenon of superdirectivity and to the method of auxiliary sources mas our study sheds light on the unusual nature of electromagnetic waves generated by currents with very rapid spatial variations subject to the condition that the discretization is fine we treat th

a repository of equations with cosine sine compactons nonlinear evolution equations with cosine sine compacton solutions are reviewed including the rosenau hyman equation and generalizations of korteweg de vries camassa holm boussinesq benjamin bona mahony klein gordon and other equations each equation is generalized to three dimensions and the conditions for its cosine solitary waves to be either a compacton or a soliton are determined several equations claimed in the literature to be different among them are found to be equivalent

new solitary wave solutions with compact support for the kdv like k m n equations with fully nonlinear dispersion in this paper a new method different from the adomian decomposition method namely the extend sine cosine method is proposed to investigate the compacton solutions of the kdv like equations with fully nonlinear dispersion k m n equations u t u m x u n x x x 0 the new exact solitary wave solutions with compact support of the equations are found by our new method the two special cases k 2 2 and k 3 3 are chosen to illustrate the concrete scheme of our approach in k m n equations an entirely new general formulas for the solutions of k m n equations for all types where m n are established our results include not only some known results in literature as special cases but also some new exact special solutions the method presented by this paper is suitable for studying compacton solutions of some other equations

observations on the tanh coth expansion method for finding solutions to nonlinear evolution equations abstract the tanh coth expansion method for finding solitary travelling wave solutions to nonlinear evolution equations has been used extensively in the literature it is a natural extension to the basic tanh function expansion method which was developed in the 1990s it usually delivers three types of solution namely a tanh function expansion a coth function expansion and a tanh coth expansion it is known that for every tanh function expansion solution there is a corresponding coth function expansion solution it is shown that there is a tanh coth expansion solution that is merely a disguised version of the coth solution in many papers such tanh coth solutions are erroneously claimed to be new however other tanh coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh function method similar remarks apply to tan cot and tan cot expansion solutions

envelope exact solutions for the generalized nonlinear schrodinger equation with a source in this letter the generalized nonlinear schrodinger gnls equation phase locked a source ei t is investigated firstly we reduce this equation to a second order non homogeneous nonlinear ordinary differential equation via a plane wave transformation and some constraint conditions then we use some fractional transformations to study exact solutions in obtaining the gnls equation as a consequence many types of exact solutions are deduced such as envelope rational solutions envelope periodic wave solutions envelope solitary wave solutions and envelope doubly periodic solutions similarly the corresponding exact solutions can also be obtained for the hirota type gnls equation with a source and their combined equation

exact solutions for the nonlinear schrodinger equation with variable coefficients using the generalized extended tanh function the sine cosine and the exp function methods abstract in this article we find the exact traveling wave solutions of the generalized nonlinear schrodinger gnls equation with variable coefficients using three methods via the generalized extended tanh function method the sine cosine method and the exp function method the main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation

convergence of relaxed parallel multisplitting methods abstract multisplitting methods are parallel methods for the solution of a linear system ax b it has been observed that the convergence of multisplitting methods is often improved if some kind of relaxation is used we investigate two different variants of relaxed multisplitting methods if a is an h matrix these methods converge if the relaxation parameter is from an interval 0 0 with 0 1

optimal currents on arbitrarily shaped surfaces an optimization problem has been formulated to find a resonant current extremizing various antenna parameters the method is presented on but not limited to particular cases of gain g quality factor q gain to quality factor ratio g q and radiation efficiency eta of canonical shapes with conduction losses explicitly included the rao wilton glisson basis representation is used to simplify the underlying algebra while still allowing surface current regions of arbitrary shape to be treated by switching to another basis generated by a specific eigenvalue problem it is finally shown that the optimal current can in principle be found as a combination of a few eigenmodes the presented method constitutes a general framework in which the antenna parameters expressed as bilinear forms can automatically be extremized

on methods to determine bounds on the q factor for a given directivity this paper revisit and extend the interesting case of bounds on the q factor for a given directivity for a small antenna of arbitrary shape a higher directivity in a small antenna is closely connected with a narrow impedance bandwidth the relation between bandwidth and a desired directivity is still not fully understood not even for small antennas initial investigations in this direction have related the radius of a circumscribing sphere to the directivity and bounds on the q factor have also been derived for a partial directivity in a given direction in this paper we derive lower bounds on the q factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semidefinite relaxation sdr techniques we also show that the relaxed solution is also a solution of the original problem of determining the lower q factor bound for a total desired directivity sdr can also be used to relax a class of other interesting nonconvex constraints in antenna optimization such as tuning losses and front to back ratio we compare two different new methods to determine the lowest q factor for arbitrary shaped antennas for a given total directivity we also compare our results with full electromagnetic simulations of a parasitic element antenna with high directivity

nonlinear waves and solitons in physical systems abstract advances in nonlinear science have been plentiful in recent years in particular interest in nonlinear wave propagation continues to grow stimulated by new applications such as fiber optic communication systems as well as the many classical unresolved issues of fluid dynamics what is arguably the turning point for the modern perspective of nonlinear systems took place at los alamos over 40 years ago with the pioneering numerical simulations of fermi pasta and ulam a decade later this research initiated the next major advance of zabusky and kruskal that motivated the revolution in completely integrable systems with this in mind the conference on nonlinear waves in solitions in physical systems nwsps was organized by the center for nonlinear studies cnls at los alamos national laboratory in may of 1997 to assess the current state of the art in this very active field papers from the conference attendees as well as from researchers unable to attend the conference were collected in this special volume of physica d in this paper the contributions to the conference and to this special issue are reviewed with an emphasis on the many unifying principles that all these works share

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

a finite difference scheme for the k 2 2 compacton equation the k 2 2 equation introduced by rosenau and hyman is a wave equation that possesses solutions compactons that vanish outside a bounded interval of the spatial axis a finite difference scheme for this equation is suggested that can successfully cope with compacton interactions leading to negative waves we show rigorously that in those interactions a loss of smoothness of the solution necessarily takes place

the tanh method exact solutions of the sine gordon and the sinh gordon equations in this work we use the tanh method for traveling wave solutions of the sine gordon and the sinh gordon equations several exact solutions of distinct physical structures are obtained the method is powerful with minimal algebra work and is demonstrated for four models

solutions of compact and noncompact structures for nonlinear klein gordon type equation the focusing and the defocusing branches of nonlinear klein gordon type equation kg n n are considered a framework is implemented to show that the first model exhibits compactons solitons that do not have exponential tails whereas the second model demonstrates solitary patterns solutions the two variants of kg n n equation will be examined in one and higher dimensions general formulas will be developed to present a fairly complete understanding of the solutions of compact and noncompact structures

self similar radiation from numerical rosenau hyman compactons the numerical simulation of compactons solitary waves with compact support is characterized by the presence of spurious phenomena as numerically induced radiation which is illustrated here using four numerical methods applied to the rosenau hyman k p p equation both forward and backward radiations are emitted from the compacton presenting a self similar shape which has been illustrated graphically by the proper scaling a grid refinement study shows that the amplitude of the radiations decreases as the grid size does confirming its numerical origin the front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters the amplitude of the radiations decreases exponentially in time being characterized by a nearly constant scaling exponent an ansatz for both the backward and forward radiations corresponding to a self similar function characterized by the scaling exponent is suggested by the present numerical results

m functions and parallel asynchronous algorithms the solution of nonlinear systems of equations fx z via parallel asynchronous algorithms is considered it is shown that when f is continuous off diagonally antitone and strictly diagonally isotone then point asynchronous iterations converge monotonically to a solution of the problem from supersolutions and subsolutions a global convergence result for asynchronous iterations when f is a continuous surjective m function is also presented

on the convergence of parallel chaotic nonlinear multisplitting newton type methods abstract a class of parallel chaotic nonlinear multisplitting newton type methods for solving the nonlinear system of equations f x 0 f d r n r n is established and its local convergence theory is presented

original and modified kernels in method of moments analyses of resonant circular arrays of cylindrical dipoles properly dimensioned circular arrays of cylindrical dipoles are known to possess very narrow resonances it is also known that analyzing such arrays using moment methods presents unique and particular difficulties as application of such methods to the usual hallen type integral equations can yield meaningless results from which no further conclusions should be drawn in the present paper we apply moment methods to properly modified integral equations and obtain much more reliable results we also observe that certain difficulties still remain and discuss them in detail

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

some convergence results for asynchronous algorithms nous presentons dans cet article des resultats de convergence des algorithmes asynchrones bases essentiellement sur la notion classique de contraction nous generalisons en particulier tous les resultats de convergence de ces algorithmes qui font l hypothese de contraction en norme vectorielle qui recemment a ete tres souvant utilisee par ailleurs l hypothese de contraction en norme vectorielle peut se trouver difficile voire impossible a verifier pour certains problemes qui peuvent etre cependant abordes dans le cadre de la contraction classique que nous adoptons in this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction we generalize in particular all convergence results for those algorithms which are based on the vectorial norm hypothesis in wide spread use recently certain problems for which the vectorial norm hypothesis can be difficult or even impossible to verify can nontheless be tackled within the scope of the classical contraction that we adopte

on two types of convergence in the method of auxiliary sources the method of auxiliary sources mas is often applied to problems involving an externally illuminated smooth perfect electric conductor pec one seeks to approximately satisfy the boundary condition on the pec surface using auxiliary sources located inside the pec surface usually the underlying auxiliary surface is also smooth and closed the currents on the auxiliary sources mas currents are the initial unknowns once they have been found one can easily determine the field due to them mas field at all points external to the auxiliary surface and in particular at all points external to the pec scatterer we show that in the limit n it is possible to have a convergent mas field together with divergent mas currents and that this phenomenon is accompanied by an abrupt behavior of the limiting value of the mas field we show this possibility through an analytical study of a two dimensional scattering problem involving a circular cylinder in which mas fields and currents can be determined explicitly the analytical study proceeds from first principles it involves fundamental electromagnetics and relatively simple mathematical manipulations numerical results supplement the analytical study and demonstrate the nature of the aforementioned divergence our study sheds light on other aspects of mas in particular it establishes interesting similarities and differences between mas and its continuous version and reveals many similarities between mas currents and numerical solutions of hallen s integral equation with the approximate kernel

solitary solutions periodic solutions and compacton like solutions using the exp function method in this paper the exp function method is used for seeking solitary solutions periodic solutions and compacton like solutions of nonlinear differential equations the combined kdv mkdv equation and the liouville equation are chosen to illustrate the effectiveness and convenience of the proposed method

a note on generalized nonlinear diagonal dominance in this paper an open problem proposed by a frommer about nonlinear generalized diagonal dominance is solved on some weak restriction a counterexample is presented if such a restriction is omitted and some new properties of nonlinear generalized diagonally dominant functions are investigated

the monotone convergence of a class of parallel nonlinear relaxation methods for nonlinear complementarity problems abstract we set up a class of parallel nonlinear multisplitting aor methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems the different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems the two sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown and sufficient conditions guaranteeing the methods to converge globally are discussed finally a lot of numerical results show that our new methods are feasible and efficient

transverse compactlike pulse signals in a two dimensional nonlinear electrical network we investigate the compactlike pulse signal propagation in a two dimensional nonlinear electrical transmission network with the intersite circuit elements both in the propagation and transverse directions acting as nonlinear resistances model equations for the circuit are derived and can reduce from the continuum limit approximation to a two dimensional nonlinear burgers equation governing the propagation of the small amplitude signals in the network this equation has only the mass as conserved quantity and can admit as solutions cusp and compactlike pulse solitary waves with width independent of the amplitude according to the sign of the product of its nonlinearity coefficients in particular we show that only the compactlike pulse signal may propagate depending on the choice of the realistic physical parameters of the network and next we study the dissipative effects on the pulse dynamics the exactness of the analytical analysis is confirmed by numerical simulations which show a good agreement with results predicted by the rosenau and hyman k 2 2 equation

elementary functions for constructing exact solutions to nonlinear partial differential equations with applications to nonlinear schrodinger type and mhd equations abstract in this paper we present an improvement to those methods based on the using of elementary functions like exponential trigonometric and hyperbolic functions in obtaining exact solutions to nonlinear partial differential equations npdes the improved method is applied to stable nonlinear schrodinger nls unstable nls generalized nls high order nls and derivative nls equations new solutions for these equations are obtained the obtained solutions are more general than a wide class of previous solutions solutions of a derivative nls equation that describes the large amplitude solitons propagating in an arbitrary direction in a high hall plasma are also obtained moreover the method is applied to magnetohydrodynamics mhd equations describing an ideal incompressible flow in the steady state one of the most important advantages of the solution method presented here is it deals with several types of nonlinearities associated with pdes without making a transformation of the original equation to another one

on the method of modified equations i asymptotic analysis of the euler forward difference method the method of modified equations is studied as a technique for the analysis of finite difference equations the non uniqueness of the modified equation of a difference method is stressed and three kinds of modified equations are introduced the first modified or equivalent equation is the natural pseudo differential operator associated to the original numerical method linear and nonlinear combinations of the equivalent equation and their derivatives yield the second modified or second equivalent equation and the third modified or simply modified equation respectively for linear problems with constant coefficients the three kinds of modified equations are equivalent among them and to the original difference scheme for nonlinear problems the three kinds of modified equations are asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step as small parameter yields exactly the same results in this paper both regular and multiple scales asymptotic techniques are used for the analysis of the euler forward difference method and the resulting asymptotic expansions are verified for several nonlinear autonomous ordinary differential equations it is shown that when the resulting asymptotic expansion is uniformly valid the asymptotic method yields very accurate results if the solution of the leading order equation is smooth and does not blow up even for large step sizes

the extended tanh method and its applications for solving nonlinear physical models the extended tanh method with a computerized symbolic computation is used for constructing the travelling wave solutions of coupled nonlinear equations arising in physics the obtained solutions include solitons kinks and plane periodic solutions the applied method will be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics

two dimensional highly directive currents on large circular loops properties of idealized two dimensional current distributions on circular loops are investigated analytically via the solution of a constrained optimization problem the directivity in the far field is maximized under a fixed c n t where n is the integral of the square of the current magnitude and t is the total radiated power c enters the ensuing fourier series for the current implicitly through a lagrange multiplier for non negative and large electrical radius ka the directivity and the current are evaluated approximately via combined use of the poisson summation formula and the mellin transform technique as a result a geometrical ray representation for the current is derived for the case of directivities that are slightly larger than that of the uniform distribution the analysis indicates certain advantages of large radiating structures for moderate values of the constraint c in the limit c of oseen s einstein needle radiation an asymptotic formula for the directivity is obtained pos

on exact travelling wave solutions for two types of nonlinear k n n equations and a generalized kp equation in this paper we study two types of genuinely nonlinear k n n equations and a generalized kp equation by developing a mathematical method based on the reduction of order of nonlinear differential equations we derive general formulas for the travelling wave solutions of the three equations the compactons solitary patterns solitons and periodic solutions obtained are expressed analytically it is shown that the y and z components of the wave number vectors in the travelling wave solutions of the generalized kp equation remain free and arbitrary constants the work generalizes the known results of travelling wave solutions for the three equations

comparison of brown s and newton s method in the monotone case in many cases when newton s method applied to a nonlinear sytemf x 0 produces a monotonically decreasing sequence of iterates brown s method converges monotonically too we compare the iterates of brown s and newton s method in these monotone cases with respect to the natural partial ordering it turns out that in most of the cases arising in applications brown s method then produces better iterates than newton s method

time stepping in petrov galerkin methods based on cubic b splines for compactons abstract four numerical methods with first to fourth order of accuracy have been developed for the time integration of the rosenau hyman k 2 2 equation the error in the solution and the invariants for the propagation of one compacton and the stability in collisions among compactons have been studied using these methods numerically induced radiation has also been characterized by means of wavefront velocity and wavefront amplitude showing that the self similarity of the radiation wavepackets observed in the numerical results is a consequence of the time stepping method among the four methods studied in this paper the best results in terms of accuracy computational cost and stability have been obtained by means of using the second order time integration method

solitary wave solutions of the generalized shallow water wave gsww equation by hirota s method tanh coth method and exp function method abstract the generalized short wave equation gsww is studied by three distinct methods the hirota s bilinear method is used to derive multiple soliton solutions for the completely integrable forms of the gsww equation the tanh coth method is used to obtain single soliton solutions for this equation the exp function method is also applied to derive a variety of travelling wave solutions with distinct physical structures for this non linear evolution equation

stability and dynamical properties of rosenau hyman compactons using pade approximants we present a systematic approach for calculating higher order derivatives of smooth functions on a uniform grid using pade approximants we illustrate our findings by deriving higher order approximations using traditional second order finite difference formulas as our starting point we employ these schemes to study the stability and dynamical properties of k 2 2 rosenau hyman compactons including the collision of two compactons and resultant shock formation our approach uses a differencing scheme involving only nearest and next to nearest neighbors on a uniform spatial grid the partial differential equation for the compactons involves first second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth order methods which differ in the possibility of increasing the degree of accuracy or not of one of the spatial derivatives to sixth order a method designed to reduce round off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity for those problems the different choices lead to different amounts of spurious radiation and we compare the virtues of the different choices

highly directive current distributions general theory a theoretical scheme for studying the properties of localized monochromatic and highly directive classical current distributions in two and three dimensions is formulated and analyzed for continuous current distributions it is shown that maximizing the directivity d in the far field while constraining c5n t where n is the integral of the square of the magnitude of the current density and t is proportional to the total radiated power leads to a fredholm integral equation of the second kind for the optimum current this equation is a useful analytical tool for studying currents that produce optimum directivities above the directivity of a uniform distribution various consequences of the present formulation are examined analytically for essentially arbitrary geometries of the current carrying region in particular certain properties of the optimum directivity are derived and differences between the continuous and discrete cases are pointed out when c the directivity tends to infinity monotonically in accord with oseen s einstein needle radiation s1063 651x 98 02108 4

a study on compacton like solutions for the modified kdv and fifth order kdv like equations in this work we study compacton like solutions for the modified kdv and fifth order kdv like equations we present compacton like solutions of the integrable nonlinear equations although the behavior of the obtained solution is reminiscent of the solitons yet its second derivative is discontinuous at the boundaries a feature characterizing the compactons

a construction of compact and noncompact solutions for nonlinear dispersive equations of even order a construction of compact and noncompact solutions for nonlinear dispersive partial differential equations of even order is considered two model equations of even orders k 4 are adopted to carry out this study the analysis reveals the presence of distinct roots of different indices that play a significant role in the solutions

a class of nonlinear fourth order variant of a generalized camassa holm equation with compact and noncompact solutions abstract in this paper we study a class of nonlinear fourth order analogue of a generalized camassa holm equation it is shown that this class gives compactons conventional solitons solitary patterns and periodic solutions it is also found that the qualitative change in the physical structure of solutions depends mainly on the exponent of the wave function u x t positive or negative and on the coefficient of u n as well

generalized nonlinear diagonal dominance and applications to asynchronous iterative methods abstract we introduce a concept of generalized diagonal dominance for nonlinear functions as in the linear case this brings together several apparently different classes of nonlinear functions such as strictly diagonally dominant functions and certain m functions with our concept we easily obtain a quite far reaching result on the global convergence of asynchronous iterative methods for finding zeros of nonlinear functions special cases include some known and several new convergence results for special iterative methods such as the nonlinear jor sor and ssor method

compactons structures for fifth order kdv like equations in higher dimensions in this paper we study a variant of the fifth order kdv equation fkdv that exhibits compactons solitons with finite wave lengths the work formally shows how to construct compact dispersive structures in higher dimensions two sets of general formulas for compactons solutions that are of substantial interest are developed for this variant fk n n for all positive integers n n 1

computations of soliton solutions and periodic solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in the present paper the focusing branch of the genuinely nonlinear dispersive k n n equation is studied in one two and three dimensional spaces in the case of 0

asymptotic analysis of finite difference methods with this article we want to advocate the use of asymptotic methods for the analysis of finite difference schemes we present several examples to demonstrate the applicability of the approach advantages over the modified equation and truncation error analysis are pointed out