explicit series solutions to nonlinear evolution equations the sine cosine method in this paper a sine cosine method is used to construct many periodic and solitary wave solutions to two nonlinear evolution systems the coupled quadratic nonlinear equations and the coupled klein gordon schrodinger equations under different parameter conditions explicit formulas for some new periodic and solitary wave solutions are successfully obtained the proposed solutions are found to be important for the explanation of some practical physical problems

abundant new exact solutions for the 3 1 dimensional jimbo miwa equation in this paper by using the generalized riccati equation mapping method and picking up its new solutions authors obtain abundant new exact solutions including kink solutions periodic form solutions soliton like solutions and rational solutions to a 3 1 dimensional jimbo miwa equation respectively

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

ensemble averages of power flow in randomly excited coupled beams the transmission of transverse vibrational energy between two coupled beams subjected to random excitation is considered extensive numerical results are given for the frequency decomposition of power flow between the beams the power flow is a function of the three non dimensional parameters describing frequency 1 where 1 is the fundamental resonance frequency of beam one length ratio l 2 l 1 and damping or modal overlap ratio single frequency and octave band averages are shown for various values of l 2 l 1 and means and variances are calculated for the ensemble of systems corresponding to a uniform distribution of 1 l 2 l 1 2 various approximate results based on modal analysis and on sea are compared with the exact results

symmetry analysis of the infeld rowlands equation a fourth order nonlinear evolution equation in 2 1 dimensions arising in the study of soliton stability is analyzed its symmetry group is shown to be infinite dimensional and is used to obtain particular solutions the equation is shown not to have the painlev e property

a generalized weierstrass elliptic function expansion method for solving some nonlinear partial differential equations the present paper deals with families of non trivial solutions of the equation email protected 2 pw 4 x qw 2 x r on the basis of these solutions a direct and generalized algebraic algorithm is described for constructing the new solutions of some nonlinear partial differential equations nlpdes subsequently many new and more general exact solutions in terms of the weierstrass elliptic function x g 2 g 3 are obtained the method can be applied to other nlpdes in mathematical physics

explicit periodic solitary wave solutions for the 2 1 dimensional boussinesq equation in this paper 2 1 dimensional boussinesq equation is investigated by using homoclinic test method with the aid of maple new explicit periodic solitary wave solutions are obtained moreover mechanical feature of wave is exhibited

response of coupled basic one dimensional dynamic systems in a recent paper a formalism was developed by the authors for accounting for the response of multiple coupled dynamic systems the dynamic systems were considered basic and one dimensional the impedances were assumed to be uniform over the spatial extents of the dynamic systems and the propagation mode in each dynamic system was assumed to be simple and defined by a single speed in this paper the formalism is slightly extended to accommodate external drives that are applied within the coupling junctions that separate dynamic systems and to ascertain the response within these junctions were the need to arise a junction is considered to be a boundary at which a number of dynamic systems may terminate a boundary in turn may be composed of a number of elementary structural components which are stacked in a prescribed manner the analytical procedure adopted for the extension is based on the concept of blocking the interfaces between a boundary and the dynamic systems that it terminates the coupling across a boundary is then accounted for by assigning appropriately determined response velocities on these interfaces in determining these response velocities the external drive components within the boundary are accommodated and the response components within the boundary are yielded as by products

on the extended applications of homogenous balance method in this paper we study the travelling wave reductions for certain 2 1 and 3 1 dimensional physically important nonlinear evolutionary equations by using the recently proposed homogenous balance method hbm through this analysis we explore certain new solutions for the equations we have studied

random point excitation of coupled beams numerical results are presented for the power flow between two coupled beams one of which is excited at a point by a random force frequency spatial over the excitation point and ensemble by varying the relative lengths of the beams averages are compared with each other and with the results from simple statistical models such as sea the mean values agree well and the standard deviations are surprisingly small

comment on on the extended applications of homogeneous balance method in this letter we show that all results presented in senthilvelan s paper can be actually obtained by a direct method

new soliton like solutions to the potential kadomstev petviashvili pkp equation in this paper new soliton like solutions are obtained for 2 1 dimensional potential kadomstev petviashvili pkp equation by using the symbolic computation method developed by gao and tian solitary wave solutions obtained in appl math comput 123 2001 29 are merely a special case in this paper the method can also be extended to other types of nolionear evolution equations in mathematical physics

applications of a further extended tanh method by using a further extended tanh method chaos solitons fract 17 2003 669 and symbolic computation system maple we obtain abundant new explicit exact solutions of the 2 1 dimensional burgers equation and the 2 1 dimensional boussinesq equation the new solutions including soliton like solutions period form solutions and some other solutions

confinement of vibration by one dimensional disorder ii a numerical experiment on different ensemble averages abstract when producing theoretical estimates of the effect of irregularity on the vibrational behaviour of a structure as has been described previously 1 3 one aims to predict the behaviour of a typical irregular structure within the set considered it might be thought that this would correspond to the ensemble averaged behaviour over the whole set but this need not be the case in fact there are several different possible ways of taking the ensemble average which can produce remarkably different results some of these do indeed correspond to the typical member of the ensemble but some of them certainly do not since rare configurations giving very large contributions to the average distort the answer this problem is investigated here via a numerical experiment on a very simple system the object is to complement the discussion in a companion paper 4 which gives theoretical analysis the aims here are threefold to know which average is the most appropriate in a given context to understand why the other averages are different and to identify the anomalous configurations making them different so that these can be avoided in designing real structures a by product is a better understanding of the averaging procedures used in the past it has not always been recognized that these various averages can give radically different answers and one can find instances where what was used was perhaps the easiest approach rather than the most appropriate one in addition the numerical experiment described here gives a good illustration of the basic phenomenon of anderson localization in an acoustic context

confinement of vibration by one dimensional disorder i theory of ensemble averaging abstract the use of ensemble averaging procedures in studying the dynamics of structurally irregular mechanical systems is discussed it is found that taking a linear average over the ensemble does not always yield the behaviour of a typical member of that ensemble under certain circumstances there are occasional members with properties so exceptional as to weight the average appreciably and the linear ensemble average can then be seriously misleading the effect is illustrated by the response and transmission properties of two simple mechanical models a system of coupled oscillators with varying natural frequencies and a vibrating string or bending beam with irregularly spaced mass and spring constraints the distinction between the ensemble average and the typical value is important in understanding the phenomenon of anderson localization described previously 1 3 by using these two models this paper provides some analytic results while an accompanying paper 4 provides complementary results from a numerical study of the coupled oscillator model

derivation of statistical energy analysis from radiative exchanges abstract this paper is concerned with the derivation of sea equations from structural ray equations rays are assumed to be uncorrelated leading to the additivity of energy inside all subsystems the energy density is the sum of a direct field from driving forces a reflected field from the boundary and a transmitted field from adjacent subsystems assuming a rain on the roof excitation and a compact shape for subsystems actual and fictitious sources on the boundary are found to be constant furthermore if the attenuation of rays during a mean free path normalized attenuation factor is light the field becomes diffuse i e homogeneous and isotropic the net exchanged power between two adjacent subsystems is then proportional to the difference of energy densities and therefore to the difference of modal energies the derived proportionality coefficient is consistent with the well known formula for coupling loss factor in terms of transmission factors these results are illustrated by a numerical simulation for a multi plate system finally the validity domains of sea and the ray theory are discussed and particularly the diffuse field assumption

are all the equations of the kadomtsev petviashvili hierarchy integrable the kadomtsev petviashvili kp hierarchy is an infinite set of nonlinear partial differential equations in which the number of independent variables increases indefinitely as one proceeds down the hierarchy since these equations were obtained as part of a group theoretical approach to soliton equations it would appear that the kp hierarchy provides integrable scalar equations with an arbitrary number of independent variables it is shown by investigating a specific equation in 3 1 dimensions that the higher equations in the kp hierarchy are only integrable in a conditional sense the equation under study taken in isolation does not pass certain well known and reliable integrability tests thus applying painleve analysis we find that solutions exist allowing movable critical points furthermore solitary wave solutions are shown to exist that do not behave like solitons in multiple collisions on the other hand if the dependence of a solution on the first 2 1 variables is restricted by the fact that it should also satisfy the kp equation itself then the integrability conditions in the other dimensions are satisfied conditional integrability thus means that linear techniques will provide only those solutions of equations in the hierarchy that simultaneously satisfy lower equations in the same hierarchy

power flow between two continuous one dimensional subsystems a wave solution abstract the power flow between two point coupled wave bearing subsystems is determined by using a wave approach the subsystems are one dimensional in that each supports just one wave mode and are described by a reflection coefficient from which in certain circumstances the modal overlap and modal density can be defined as continuous functions of frequency the coupling element is described by a reflection coefficient and attention is focused on the case of conservative coupling time harmonic point forces or rain on the roof excitations may act on the subsystems uncertainty exists in the properties of the subsystems which are assumed to be drawn from ensembles of similar subsystems the exact power flow and the ensemble statistics are seen to depend on the magnitudes of the subsystem and coupling reflection coefficients for some particular cases the maximum and minimum power flows are examined together with the ensemble mean and geometric mean the cumulative probability distribution and the probability density function for a given power incident upon the coupling the ensemble mean power flow through the coupling is always less than that expected from a normal sea wave approach due to power re radiation the differences are largest when the damping is light and the coupling strong for a given level of excitation power re radiation effects are also apparent for the ensemble mean power flow from an infinite subsystem to a finite subsystem in the opposite case the ensemble mean power flow from a finite to an infinite subsystem is greater than that between two infinite subsystems due to power re injection the differences are largest for light damping and for weak coupling finally the case where there is uncertainty in one subsystem only is considered

efficient exceedance probability computation for randomly uncertain nonlinear structures with periodic loading abstract a method is developed to compute low level response amplitude exceedance probabilities associated with uncertain nonlinear structures with random parameters and deterministic periodic forcing emphasis is focused on accurate and efficient computation in the tails of the exceedance probability distribution function associated with the largest possible response of one displacement variable for unspecified forcing frequency and normally distributed parameters this gives a measure of system reliability when a large amplitude response exceedance of a specified threshold is designated as the mode of failure the method exploits the first order reliability method form in which the failure surface is constructed via the harmonic balance method hbm this combined approach is tested on a duffing oscillator with harmonic forcing and up to three uncertain parameters for which the frequency of multiple solution maximum amplitude is found directly and the probability computed via the hasofer lind reliability index the accuracy of the proposed hbm form in the tails of the amplitude exceedance probability is shown for the duffing example to be acceptably accurate whereas the efficiency is shown to be around 1000 times faster than direct integration and around 200 times faster than monte carlo simulation

comparison of an integral equation on energy and the ray tracing technique in room acoustics this paper deals with a comparison of two room acoustic models the first one is an integral formulation stemming from power balance and the second is the ray tracing technique with a perfectly diffuse reflection law the common assumptions to both models are the uncorrelated wave hypothesis and the perfectly diffuse reflection law the latter allows the use of these methods for nondiffuse fields beyond the validity domain of sabine s formula comparisons of numerical simulations performed with the softwares rayon and ceres point out that these results are close to each other and finally a formal proof is proposed showing that both methods are actually equivalent

symbolic computation and new families of exact travelling solutions for the kawahara and modified kawahara equations in this paper we consider the nonlinear evolution equations such as kawahara equation and modified kawahara equation by using the tanh method and an exp function method the travelling wave solutions for the these equations are presented new exact travelling solutions are explicitly obtained with the aid of symbolic computation the obtained solutions include compactons solitons solitary patterns and periodic solutions

systems of ordinary differential equations which generate an order preserving flow a survey of results this article consists of a survey of results concerning the qualitative behavior of solutions of systems of ordinary differential equations which generate an order preserving flow we restrict our consideration to partial orderings on r n induced by any one of its orthants a flow preserves ordering if any two solutions x t and y t are ordered x t leqq y t for all t 0 whenever x 0 leqq y 0 many of the important results for such systems have only recently been obtained principally by m w hirsch who pointed out the tendency of their solutions to converge to equilibrium less well known are some global geometric constraints on the stable manifold of an equilibrium and the existence of heteroclinic orbits connecting ordered equilibria a particularly striking result for this class of systems is the easily computable necessary and sufficient condition for stability of an equilibrium one of our main goals is to show that by allowing partial orderings on r n generated by orthants

an approach to the theoretical background of statistical energy analysis applied to structural vibration rayleigh s classical approach to the study of vibration of systems having a finite number of degrees of freedom is applied to the problem of coupling of subsystems in a complicated structure in order to probe the regions of applicability of the approach to vibration analysis usually known as statistical energy analysis sea the classical method has advantages of simplicity and rigor over previous approaches to the background of sea in certain cases and provides extensions and simplifications in several areas of the theory it also suggests modifications to sea modeling strategy depending on the type of coupling involved even when that coupling is weak so that earlier analyses might be thought to apply

vibration isolation from irregularity in a nearly periodic structure theory and measurements this article describes the theory and a simple experiment carried out to demonstrate the phenomenon of anderson localization in an acoustical context this is an effect whereby the propagation of vibration in a structure which is not entirely regular is impeded by the irregularities giving rise on the average to an exponential decay of vibration level away from the driving point even in the absence of any dissipation the structure used in the experiment was a stretched string with masses attached to it this string was studied with regular spacings of the masses and after the masses had been moved in a controlled way to provide a small degree of irregularity in both cases the transmission of energy from end to end of the string was measured as a function of frequency and also the mode shapes in the second and fourth passbands were measured so as to demonstrate the underlying physics of the localization phenomenon in which the individual modes making up each passband change from being extended throughout the structure in the regular case to being localized in specific areas of the structure in the presence of irregularity all measurements yielded satisfactory agreement with the theoretical predictions

uncertainty propagation in sea for structural acoustic coupled systems with non deterministic parameters abstract considering limited available information on uncertainties in structural acoustic coupled systems two methods namely the vertex method and the legendre orthogonal polynomial based method for predicting their dynamic behavior are developed based on the statistical energy analysis sea approach for the vertex method an efficient program for determining coordinates of all vertices of the rectangular spanned by entries of the involved interval input vector is coded which is well suited for an interval input vector in arbitrary dimension instead of calculating the extremum of the response of interest a method for determining its minimal and maximal point vectors dimension by dimension with respect to uncertain parameters is proposed based on the legendre orthogonal polynomial approximation following the theoretical analysis of the accuracy and efficiency of the proposed methods their validation is performed by one numerical example and two applications

in plane free vibration analysis of combined ring beam structural systems by wave propagation this paper presents a systematic wave propagation approach for the free vibration analysis of networks consisting of slender straight and curved beam elements and complete rings the analysis is based on a ray tracing method and a procedure to predict the natural frequencies and mode shapes of complex ring beam networks is demonstrated in the wave approach the elements are coupled using reflection and transmission coefficients and these are derived for discontinuities encountered in a mems rate sensor consisting of a ring supported on an array of folded beams these are combined taking into account wave propagation and decay to provide a concise and efficient method for studying the free vibration problem a simplification of the analysis that exploits cyclic symmetry in the structure is also presented the effects of decaying near field wave components are included in the formulation ensuring that the solutions are exact to illustrate the effectiveness of the approach several numerical examples are presented the predictions made using the proposed approach are shown to be in excellent agreement with a conventional fe analysis

comparison of statistical and interval analysis for the energy flow uncertainties in structural vibrating systems in this paper the energy flow confidence between two structural multimodal systems coupled by a joint with uncertain parameters is computed by two different methods the first one assumes that the joint parameters perturbed randomly the statistical moments of the energy flow are calculated by an analytical procedure the second one uses interval analysis the joint parameters are considered interval variables and the interval of the energy flow is determined the properties of the statistical and interval solution are investigated and compared

group theoretical analysis of dispersive long wave equations in two space dimensions abstract the symmetry algebra of an integrable dispersive long wave equation in two space dimensions is shown to be infinite dimensional and to have a kac moody virasoro structure the corresponding symmetry group is used to generate a large number of new solutions in particular solitons kinks and periodic waves these waves have wave crests of quite general shapes the results are compared to those for a nonintegrable two space dimensional dispersive long wave equation for which the symmetry group is finite dimensional and wave crests are always straight lines

exact solutions of coupled nonlinear klein gordon equation abstract in this paper we employ the general integral method for traveling wave solutions of coupled nonlinear klein gordon equations based on the idea of the exact jacobi elliptic function a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations the solutions obtained include solitons periodic solutions and jacobi elliptic function solutions

a note on new travelling wave solutions to the ostrovsky equation in a recent paper by yasar e yasar new travelling wave solutions to the ostro vsky equation appl math comput 216 2010 3191 3194 new travelling wave solutions to the transformed reduced ostrovsky equation are presented in this note it is shown that some of these solutions are disguised versions of known solutions

the statistics of power flow between two continuous one dimensional subsystems abstract the power flow between two continuous subsystems is examined using a wave solution 1 one of the subsystems is excited by time harmonic forces and both subsystems can support only one power transmitting wave mode uncertainty exists in the subsystems which are assumed to be drawn at random from ensembles those ensembles members that have a natural frequency at the excitation frequency are determined the particular members that are resonant are seen to depend on the strength of coupling the statistics of power flow are considered in particular the maximum minimum ensemble arithmetic and geometric means the variance and the cumulative probability distribution of the power flow the maximum power flow undergoes a qualitative change at a particular coupling strength for weak coupling the peak power flows occur at the uncoupled natural frequencies while for stronger coupling they occur at the coupled frequencies the ensemble average power flow may be significantly less than that expected from a normal sea approach due to power re radiation especially for a lightly damped receiving subsystem and strong coupling conversely it may be much greater due to power re injection which occurs particularly for a lightly damped excited subsystem and weak coupling the power flow variance is largest for small damping and weak coupling under which circumstances the cumulative probability distribution has an infrequent but dominant tail of very large power flows

on the existence and uniqueness of connecting orbits the question of existence and uniqueness of orbits connecting two critical points of a vector field arises in ordinary and partial differential equations 11 2 5 using monotonicity and stable manifold theory we prove an n dimensional result which is the same as that of conlon 2 except we replace his c2 vector field with a c vector field and we weaken his positivity assumption on the off diagonal terms of the jacobian of the vector field conlon s result is a generalization of a 2 dimensional result of conley and smoller l

the statistics of waves propagating in a one dimensional random medium we consider the one dimensional scattering of waves in a time independent random medium the waves considered are time harmonic it is assumed that the wavelength of the waves and the correlation length of the scatterers are small compared with the distance required for significant scattering stochastic process theory is used to investigate the statistics of the wavefield the problem of a wave incident on a length of random medium is investigated in two cases the first is where the medium is backed by a perfectly reflecting boundary here the intensity is shown to be a product of two factors an exponential term that decays into the medium and the exponential of a brownian motion that describes the fluctuations of intensity with different realizations of the random medium because a brownian motion has a normal distribution the intensity has a log normal distribution at any fixed point in the interior of the medium for a typical realization of the random medium the exponential decay leads to most of the wave energy being near the front of a long medium however it is shown that the average intensity is independent of position in the medium this is because of the long tail of the log normal distribution and comes about because the average is heavily weighted by exceptional realizations of the medium thus the average value of the intensity unlike the average of the logarithm of the intensity is not representative of the intensity in a typical realization the exponential decay of intensity is a result of the phenomenon of anderson localization which has received much attention in solid state physics the second case considered is where there is no barrier at the back of the medium for large lengths of the random medium it is shown that the transmitted intensity has an approximately log normal distribution the typical transmitted intensity is exponentially small as a result of localization the decay rate with length being the same as the decay rate for the previous case the average transmitted intensity is also exponentially small but with a different decay rate because of weighting by exceptional realizations the third problem discussed is that of the response of a random medium to time harmonic forcing in the interior the boundaries are taken to be perfectly reflecting and the response is found to be localized near the source for a typical realization this result is related to the existence of localized normal modes in a long medium

study on the validity region of energy finite element analysis abstract the validity domain of energy finite element analysis efea is studied in this paper the validity region and criterion of efea are studied theoretically from the formation of reverberant plane wave field one of the main assumptions of efea the studies are acquired by virtue of the equation of radiative energy transfer method a similar wave method that can express the direct field and its conversion relationship with reverberant field exactly the result shows that the sea criterion of diffuse field derived by le bot can be used as a good indicator for the efea validity numerical simulations on a rectangular plate with different physical parameters are applied to validate the criterion the validity region and the diagrams of validity of efea are assessed and discussed some noteworthy conclusions about efea are drawn

exact travelling wave solutions for a generalized zakharov kuznetsov equation in this paper by means of a proper transformation and symbolic computation we study the exact travelling wave solutions for a generalized zakharov kuznetsov gzk equation by using the extended tanh method and direct assumption method as a result rich exact travelling wave solutions which contain new kink shaped solitons bell shaped solitons periodic solutions combined formal solitons rational solutions and singular solitons for gzk equation are obtained

wave derivation of the energetics of driven coupled one dimensional dynamic systems abstract the equation of statistical energy analysis was originally derived on the basis of modal concepts in this paper a derivation of the equation on the basis of wave concepts is outlined although the new formalism is limited at present to the analysis of coupled one dimensional dynamic systems it carries details that were a priori forfeited by the previous formalism the wave approach to sea as developed in the paper reveals a formalism that can be naturally used for the analysis of net power and intensity in coupled dynamic systems this aspect of the formalism is briefly discussed

asymptotic behavior of a predator prey system with diffusion and delays abstract in this paper the asymptotic behavior of solutions of a predator prey system is determined the model incorporates time delays due to gestation and assumes that the prey disperses between two patches of a heterogeneous environment with barriers between patches and that the predator disperses between the patches with no barrier conditions are established for the permanence of the populations and the global attractivity of a positive equilibrium

extend three wave method for the 1 2 dimensional ito equation abstract in this work extend three wave method etm is used to construct the novel multi wave solutions of the 1 2 dimensional ito equation as a result three soliton solution doubly periodic solitary wave solutions periodic two solitary wave solutions are obtained it is shown that the extend three wave method may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

energy transfer for high frequencies in built up structures this paper is concerned with the prediction of vibrations at high frequencies in built up structures in the high frequency range the dynamical behaviour of structures is driven by energy transfer rather than modal aspects the description of systems in terms of energy is thus well suited and leads to closed form equations of an integral type on energy variables the numerical solution of these equations is achieved with appropriate software called ceres and the results are compared with experimental measurements on a multi plate structure

propagation of decaying waves in periodic and piecewise periodic structures of finite length abstract a new method is described for the analysis of long and complicated structures which are composed of spatially periodic units or sections of spatially periodic units the response of such a structure to external excitations is treated as a superposition of wave motions with account taken of the effects of wave reflection due to change in the construction pattern along the structure and boundary conditions since damping usually exists in a real structure a wave motion always decays as it propagates along the structure however this can cause numerical difficulties if the structure is rather long because a decaying wave appears as a growing wave in the opposite direction and since propagations in both directions must be accounted for in the analysis computational errors associated with the apparent growing waves also grow and the numerical results become meaningless in the proposed new scheme use is made of wave reflection and transmission matrices making it possible for all computations to proceed in the direction of wave propagation so that the results are always stable numerically furthermore the required computing time is greatly reduced in comparison with that of an all encompassing finite element analysis for the entire structure application of the new method is illustrated by examples

a note on abundant new exact solutions for the 3 1 dimensional jimbo miwa equation abstract we demonstrate that eight from twenty seven solutions obtained by li and dai abundant new exact solutions for the 3 1 dimensional jimbo miwa equation j math anal appl 361 2010 587 590 are wrong and do not satisfy the equation the other nineteen exact solutions are not new solutions and can be found from the well known solution

dynamical survey of a generalized zakharov equation and its exact travelling wave solutions we investigate the dynamical behavior of a generalized zakharov equation for the complex envelope of the high frequency wave and the real low frequency field by analyzing its phase portraits following a dynamical system approach in different parameter regions we depict phase portraits of a travelling wave system through discussing the bifurcation of phase portraits we unwrap explicit miscellaneous travelling waves including localized and periodic ones

symmetry reductions and new exact non traveling wave solutions of potential kadomtsev petviashvili equation with p power with the aid of maple symbolic computation and lie group method pkpp equation is reduced to some 1 1 dimensional partial differential equations in which there are linear pde with constant coefficients nonlinear pde with constant coefficients and nonlinear pde with variable coefficients using the separation of variables homoclinic test technique and auxiliary equation methods we obtain new abundant exact non traveling solutions with arbitrary functions for the pkpp

response of multiple coupled dynamic systems abstract analytical procedures are developed to investigate the nature of the response of multiple coupled dynamic systems the dynamic systems are one dimensional and are coupled at junctions the spatial extents of the dynamic systems are determined by these junctions a dynamic system terminates at these junctions the junctions are characterized by assigning reflection and transmission coefficients at the terminal positions of the dynamic systems in addition a dynamic system is characterized by a single propagation wavenumber the wavenumber may be complex accounting for possible spatial attenuation and for distributed damping in the dynamic system further damping edge damping may be accounted for by assigning non conservative coefficients at the junction quadratic forms describing the dynamics of multiple coupled dynamic systems are also presented and discussed relationship of such forms to the statistical energy analysis sea of complex dynamic systems is touched upon this paper is concerned chiefly with the development of analytical procedures examples of application of these procedures will be dealt with in subsequent publications

comparison of two non probabilistic approaches for the energy flow uncertainty in structural vibrating system two non probabilistic set theoretical methods for determining the energy flow between two structural multimodal systems coupled by a joint with uncertain parameters are presented they are based on the theories of interval mathematics and convex models the uncertain parameters of the joint are assumed to be a convex set hyper rectangle or ellipsoid for both non probabilistic methods less prior information about the uncertain nature is required than that which is required concerning the probabilistic model the properties of the standard interval arithmetic the interval taylor expansion the convex models and the monte carlo method solutions are investigated and compared

validity diagrams of statistical energy analysis abstract this paper is concerned with the validity domain of statistical energy analysis sea which is defined in terms of four criteria the mode count n and the modal overlap m must be high the normalized attenuation factor m and the coupling strength must be small the application of dimensional analysis on the governing equations of plates gives the space of dimensionless parameters in which the validity domain of sea must be delimited this domain is discussed on the basis of geometry of the surfaces delimiting it the diagrams of validity of sea are introduced and discussed a numerical simulation on a couple of rectangular plates coupled along one edge illustrates the theoretical approach

new solutions of the 3 1 dimensional jimbo miwa equation we find new exact solutions of the 3 1 dimensional jimbo miwa equation by applying the extended homogeneous balance method we also get an iterative formula of finding exact solutions this paper shows that there exist a lot of solutions for the 3 1 dimensional jimbo miwa equation

new exact solutions to the 2 1 dimensional ito equation extended homoclinic test technique exact soliton solutions to the 2 1 dimensional ito equation are studied based on the idea of extended homoclinic test and bilinear method some explicit solutions such as triangle function solutions soliton solutions doubly periodic wave solutions and periodic solitary wave solutions are obtained it shows that the 2 1 dimensional ito equation has richer solutions besides the elastic interactions of the solutions and their corresponding physical meaning are discussed

analytical solution for the power exchange between strongly coupled plates under random excitation a test of statistical energy analysis concepts the response of the structural components of a complex structure subjected to random loads is often estimated by approximate methods based on the concepts of statistical energy analysis sea to examine the fundamental sea postulates and assumptions the problem of two coupped plates is rigorously formulated and solved in terms of usual sea variables for randomly distributed loads analytical results are presented for the power flow and plate vibrational energies the formulation allows the extraction of apparent quantifies that correspond to the coupling loss factor and modal density ratio of statistical energy analysis it is demonstrated that this model can yield an understanding of the implications of basic sea assumptions results for simply supported plates clearly show the effects of internal damping and frequency on the coupling parameters

the decomposition method for solving 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation we study the solitary wave solutions of the 2 1 dimensional boussinesq equation u t t u x x u y y u 2 x x u x x x x 0 and 3 1 dimensional kp equation u x t 6u x 2 6uu x x u x x x x u y y u z z 0 in this paper by considering the decomposition scheme we first obtain the exact solitary wave solutions of the 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation for the initial conditions without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation