new periodic and soliton solutions by application of exp function method for nonlinear evolution equations in this letter the kaup kupershmidt 2 1 dimensional potential kadomtsev petviashvili shortly pkp equations are presented and the exp function method is employed to compute an approximation to the solution of nonlinear differential equations governing the problem it has been attempted to show the capabilities and wide range applications of the exp function method this method can be used as an alternative to obtain analytic and approximate solution of different types of differential equations applied in engineering mathematics

periodic polya urns the density method and asymptotics of young tableaux polya urns are urns where at each unit of time a ball is drawn and replaced with some other balls according to its colour we introduce a more general model the replacement rule depends on the colour of the drawn ball and the value of the time operatorname mod p we extend the work of flajolet et al on polya urns the generating function encoding the evolution of the urn is studied by methods of analytic combinatorics we show that the initial partial differential equations lead to ordinary linear differential equations which are related to hypergeometric functions giving the exact state of the urns at time n when the time goes to infinity we prove that these periodic polya urns have asymptotic fluctuations which are described by a product of generalized gamma distributions with the additional help of what we call the density method a method which offers access to enumeration and random generation of poset structures we prove that the law of the southeast corner of a triangular young tableau follows asymptotically a product of generalized gamma distributions this allows us to tackle some questions related to the continuous limit of random young tableaux and links with random surfaces

recurrence coefficients for discrete orthonormal polynomials and the painleve equations we investigate semi classical generalizations of the charlier and meixner polynomials which are discrete orthogonal polynomials that satisfy three term recurrence relations it is shown that the coefficients in these recurrence relations can be expressed in terms of wronskians of modified bessel functions and confluent hypergeometric functions respectively for the generalized charlier and generalized meixner polynomials these wronskians arise in the description of special function solutions of the third and fifth painleve equations

random sorting networks abstract a sorting network is a shortest path from 12 n to n 21 in the cayley graph of s n generated by nearest neighbour swaps we prove that for a uniform random sorting network as n the space time process of swaps converges to the product of semicircle law and lebesgue measure we conjecture that the trajectories of individual particles converge to random sine curves while the permutation matrix at half time converges to the projected surface measure of the 2 sphere we prove that in the limit the trajectories are holder 1 2 continuous while the support of the permutation matrix lies within a certain octagon a key tool is a connection with random young tableaux

application of the exp function method for nonlinear differential difference equations in this paper we established abundant travelling wave solutions for some nonlinear differential difference equations it is shown that the exp function method with the help of symbolic computation provides a very effective and powerful new method for discrete nonlinear evolution equations in mathematical physics

jeu de taquin dynamics on infinite young tableaux and second class particles we study an infinite version of the jeu de taquin sliding game which can be thought of as a natural measure preserving transformation on the set of infinite young tableaux equipped with the plancherel probability measure we use methods from representation theory to show that the robinson schensted knuth rsk algorithm gives an isomorphism between this measure preserving dynamical system and the one sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval we also show that the jeu de taquin paths induced by the transformation are asymptotically straight lines emanating from the origin in a random direction whose distribution is computed explicitly and show that this result can be interpreted as a statement on the limiting speed of a second class particle in the plancherel tasep particle system a variant of the totally asymmetric simple exclusion process associated with plancherel growth in analogy with earlier results for second class particles in the ordinary tasep

on characterizations of classical polynomials it is well known that the classical families of jacobi laguerre hermite and bessel polynomials are characterized as eigenvectors of a second order linear differential operator with polynomial coefficients rodrigues formula etc in this paper we present a unified study of the classical discrete polynomials and q polynomials of the q hahn tableau by using the difference calculus on linear type lattices we obtain in a straightforward way several characterization theorems for the classical discrete and q polynomials of the q hahn tableau finally a detailed discussion of a characterization by marcellan et al is presented

group similarity solutions of the lax pair for a generalized hirota satsuma equation a modified version of generalized hirota satsuma is here analytically solved using a two parameter group transformation method we here through a group symmetry transformation reduce its lax pair to a system of ordinary equations and find new solutions three similarity transformation variables are investigated for each case an analytical solution is obtained through a homogenous balance of terms in the reduced lax pair the obtained results are plotted and show a profile proper to deflagration processes well described by degasperis procesi equation

some new solitonary solutions of the modified benjamin bona mahony equation abstract in this paper we use the exp function method to construct some new soliton solutions of the benjamin bona mahony and modified benjamin bona mahony equations these equations have important and fundamental applications in mathematical physics and engineering sciences the exp function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation this method provides the concise and straightforward solution in a very easier way the results obtained in this paper can be viewed as a refinement and improvement of the previously known results

mixing times of the biased card shuffling and the asymmetric exclusion process consider the following method of card shuffling start with a deck of n cards numbered 1 through n fix a parameter p between 0 and 1 in this model a shuffle consists of uniformly selecting a pair of adjacent cards and then flipping a coin that is heads with probability p if the coin comes up heads then we arrange the two cards so that the lower numbered card comes before the higher numbered card if the coin comes up tails then we arrange the cards with the higher numbered card first in this paper we prove that for all p 1 2 the mixing time of this card shuffling is o n 2 as conjectured by diaconis and ram 2000 our result is a rare case of an exact estimate for the convergence rate of the metropolis algorithm a novel feature of our proof is that the analysis of an infinite asymmetric exclusion process plays an essential role in bounding the mixing time of a finite process

modified extended tanh function method and its applications to nonlinear equations new exact travelling wave solutions for the generalized shallow water wave equation the improved boussinesq equation and the coupled system for the approximate equations for water waves are found using a modified extended tanh function method the obtained results include rational periodic singular and solitary wave solutions

the recurrence coefficients of semi classical laguerre polynomials and the fourth painleve equation we show that the coefficients of the three term recurrence relation for orthogonal polynomials with respect to a semi classical extension of the laguerre weight satisfy the fourth painleve equation when viewed as functions of one of the parameters in the weight we compare different approaches to derive this result namely the ladder operators approach the isomonodromy deformations approach and combining the toda system for the recurrence coefficients with a discrete equation we also discuss a relation between the recurrence coefficients for the freud weight and the semi classical laguerre weight and show how it arises from the backlund transformation of the fourth painleve equation

application of the g g expansion method to 3 1 dimensional nonlinear evolution equations in this paper the g g expansion method is employed to solve the 3 1 dimensional kadomtsev petviashvili kp equation the 3 1 dimensional potential ytsf equation and the 3 1 dimensional jimbo miwa jm equation exact traveling wave solutions are obtained the traveling wave solutions are expressed in terms of hyperbolic functions the trigonometric functions and the rational functions

the isomonodromy approach to matric models in 2d quantum gravity we consider the double scaling limit in the hermitian matrix model for 2d quantum gravity associated with the measure exp sum limits j 1 n t j z 2j n geqq 3 we show that after the appropriate modification of the contour of integration the cross migdal douglas shenker limit to the painleve i equation in the generic case of the pure gravity is valid and calculate the nonperturbative parameters of the corresponding painleve function our approach is based on the wkb analysis of the l a pair corresponding to the discrete string equation in the framework of the inverse monodromy method here we extend our results which were obtained before for the particular casesn 2 3 our analysis complements the isomonodromy approach proposed by g moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself

solving the breaking soliton equation by he s variational method he s variational method is applied to obtain the soliton solutions of the breaking soliton equation where the semi inverse method is applied to establish a needed variational functional

recurrence coefficients of generalized meixner polynomials and painleve equations we consider a semi classical version of the meixner weight depending on two parameters and the associated set of orthogonal polynomials these polynomials satisfy a three term recurrence relation we show that the coefficients appearing in this relation satisfy a discrete painleve equation which is a limiting case of an asymmetric dpiv equation moreover when viewed as functions of one of the parameters they satisfy one of chazy s second degree painleve equations which can be reduced to the fifth painleve equation pv

discrete painleve equations and their appearance in quantum gravity we discuss an algorithmic approach for both deriving discrete analogues of painleve equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations as a concrete example we show that a discrete analogue of painleve i can be used to characterize similarity solutions of the kac moerbeke equation it turns out that these similarity solutions also satisfy a special case of painleve iv equation in addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions as an example we use the wkb method in the presence of two turning points of the third order to parametrize at the continuous limit the solution of painleve i in terms of the solution of discrete painleve i finally we show that these results are useful for investigating the partition function of the matrix model in 2d quantum gravity associated with the measure exp t1z2 t2z4 t3z6

a new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the exp function method abstract a new algorithm and its maple implementation aefm are presented to find exact solitary wave solutions of nonlinear partial differential equations pdes in terms of the exp function method it turns out that the program can perform the exp function method entirely automatically and output directly solitary solutions to n 1 dimensional pdes furthermore the package allows users to find desirable solutions with different input parameters the effectiveness of the algorithm is illustrated by applying it to a variety of equations

hydrodynamics and large deviation for simple exclusion processes we prove the hydrodynamical limit for weakly asymmetric simple exclusion processes a large deviation property with respect to this limit is established for the symmetric case we treat also the situation where a slow reaction creation and annihilation of particles is present

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

solitary and periodic wave solutions of calogero bogoyavlenskii schiff equation via exp function methods abstract in this paper some proficient techniques called the exp function method modified exp function method and improved modified exp function method are implemented to compute generalized solitary and periodic wave solutions of the nonlinear calogero bogoyavlenskii schiff equation it has been attempted to show the compatibility and reliability of these mathematical techniques the first partial differential equation is converted into an ordinary differential equation by a suitable transformation then a trial solution is assumed results indicate complete consistency and effectiveness of the suggested schemes

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

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

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

the g g expansion method for some nonlinear evolution equations abstract in this paper the g g expansion method is applied to the liouville sine gordon and new coupled mkdv equations to obtain their some generalized exact travelling wave solutions

the exp function method and generalized solitary solutions the exp function method is applied to a system of nonlinear partial differential equations and generalized solitary solutions with free parameters are obtained the solution procedure is simple with the help of symbolic computation

general expa function method for nonlinear evolution equations abstract this work generalizes the exponential function method in considering an arbitrary base a as opposed to the conventional base e for the exponential function the combined kdv mkdv equation is considered to reveal the effectiveness and convenience of the proposed generalization the study highlights the power of the proposed method on constructing solutions expressed in terms of exponential hyperbolic periodic symmetrical fibonacci symmetrical lucas and k fibonacci functions some of the obtained solitary wave solutions are sketched graphically

exact solutions for the generalized nonlinear heat conduction equations using the exp function method the exp function method is used to find exact solutions of the generalized nonlinear heat conduction equations the results obtained include all the solutions from the open literature as special cases

generalized solitary wave solutions for the klein gordon schrodinger equations some new generalized solitary solutions of the klein gordon schrodinger equations are obtained using the exp function method which include some known solutions obtained by the f expansion method and the homogeneous balance method in the open literature as special cases it is shown that the exp function method is a straight concise reliable and promising mathematical tool for solving nonlinear evolution equations arising in mathematical physics

diffuse scattering on graphs abstract we formulate and analyze difference equations on graphs analogous to time independent diffusion equations arising in the study of diffuse scattering in continuous media moreover we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous background problem using born series providing necessary conditions for convergence and demonstrating the process through numerous examples in addition we outline a method for finding green s functions for cayley graphs for both abelian and non abelian groups finally we conclude with a discussion of the effects of sparsity on our method and results outlining the simplifications that can be made provided that the scatterers are weak and well separated

generalized solitary and periodic wave solutions to a 2 1 dimensional zakharov kuznetsov equation abstract in this paper the exp function method is employed to the zakharov kuznetsov equation as a 2 1 dimensional model for nonlinear rossby waves the observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient the obtained results may be useful for better understanding the properties of two dimensional coherent structures such as atmospheric blocking events

combinatorial aspects of the lascoux schutzenberger tree abstract in 1982 richard stanley introduced the formal series f x in order to enumerate reduced decompositions of a given permutation stanley european j combin 5 4 1984 359 not only showed f x to be symmetric but in certain cases f x was a schur function stanley conjectured that for arbitrary f x was always schur positive edelman and greene subsequently proved this fact combinatories and algebra boulder co 1983 amer math soc providence ri 1984 pp 155 162 adv in math 63 1 1987 42 using the techniques of lascoux and schutzenberger lett math phys 10 2 3 1985 111 for computing littlewood richardson coefficients we will exhibit a new bijective proof of the schur positivity of f x

the tasep speed process in the multi type totally asymmetric simple exclusion process tasep each site ofz is occupied by a labeled particle and two neighboring particles are int erchanged at rate one if their labels are in increasing order consider the process with the initial con figuration where each particle is labeled by its position it is known that in this case a s each particle has an asymptotic speed which is distributed uniformly on 1 1 we study the joint distribution of these speeds the tasep speed process we prove that the tasep speed process is a stationary measure for the multi type tasep dynamics consequently we can describe every ergodic stationary measure as a projection of the speed process measure this generalizes previous descriptions restricted to finitely many classes by combining this result with known stationary measures for taseps with finitely many types we compute several marginals of the speed process including the joint density of two and three consecutive speeds one striking property of the distribut ion is that two speeds are equal with positive probability and for any given particle there are infinitely m any others with the same speed we also study the partially asymmetric simple exclusion process asep we prove that the states of the asep with the above initial configuration seen as permutations ofz are symmetric in distribution this allows us to extend some of our results i ncluding the stationarity and description of all ergodic stationary measures also to the asep

application of the τ function theory of painleve equations to random matrices pv piii the lue jue and cue with denoting an average with respect to the eigenvalue pdf for the laguerre unitary ensemble the object of our study is e n i a x l i l 0 i l for i 0 s and i s where x i l 1 for l i and x i l 0 other wise using okamoto s development of the theory of the painleve v equation it is shown that e n i a is a function associated with the hamiltonian therein and so can be characterized as the solution of a certain second order second degree differential equation or in terms of the solution of certain difference equations the cases 0 and 2 are of particular interest because they correspond to the cumulative distribution and density function respectively for the smallest and largest eigenvalue in the case i s e n i a is simply related to an average in the jacobi unitary ensemble and this in turn is simply related to certain averages over the orthogonal group the unitary symplectic group and the circular unitary ensemble the latter integrals are of interest for their combinatorial content also considered are the hard edge and soft edge scaled limits of e n i a in particular in the hard edge scaled limit it is shown that the limiting quantity e hard 0 s a can be evaluated as a function associated with the hamiltonian in okamoto s theory of the painleve iii equation

solutions of the generalized kdv equation with time dependent damping and dispersion solitary wave solutions are obtained for the generalized korteweg de vries gkdv equation with time dependent damping and dispersion by using the tanh coth method the exp function method and the modified sine cosine method these methods are useful and efficient and a variety of solitary wave solutions are obtained that possess variable coefficients

representations of symmetric groups and free probability abstract we consider representations of symmetric groupssqfor largeq we give the asymptotic behaviour of the characters when the corresponding young diagrams rescaled by a factorq 1 2 converge to some prescribed shape this behaviour can be expressed in terms of the free cumulants for a probability measure associated with the limit shape of the diagram we also show that the basic operations of representation theory like taking tensor products restriction or induction have a limiting behavior which can be described using the free probability theory of d voiculescu

the solitary solution of the liouville equation produced by the exp function method does not hold for all initial conditions a b s t r a c t in this paper we argue that the solitary solution of the liouville equation produced by the exp function method does not satisfy the original differential equation for all initial conditions moreover the region where the solution is correct is located entirely on a curve in the parameter plane of initial conditions we derive the explicit equation for this curve and argue that classical exp function type methods cannot identify such constraints related to initial conditions

a novel traveling wave solution for ostrovsky equation using exp function method in this paper we predict a new traveling wave solution of ostrovsky equation by using he s exp function method the method is straightforward and concise and its application shows an imminent prospective for the nonlinear problems in mathematical physics

painleve vi and hankel determinants for the generalized jacobi weight we study the hankel determinant of the generalized jacobi weight x t x 1 x for x 0 1 with 0 t 0 and based on the ladder operators for the corresponding monic orthogonal polynomials pn x it is shown that the logarithmic derivative of the hankel determinant is characterized by a jimbo miwa okamoto form of the painleve vi system

a travelling wave solution to the ostrovsky equation in this paper we consider a nonlinear evolution equation like ostrovsky equation by using the hyperbolic tangent method and an exponential function approach a travelling wave solution for the ostrovsky equation is presented it is observed that both methods lead to the same type of solution

nonlinearity as a sensitive informative marker in the enso model in this paper we use the basic idea of the exp function method to obtain an exact solution of a sea air oscillator for the enso model the effect of a nonlinear term on the properties of the el nino southern oscillation is illustrated

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

application of g g expansion method to regularized long wave rlw equation in this paper the g g expansion method with the aid of maple is used to obtain a generalized soliton solution for the generalized regularized long wave rlw equation each of the obtained solutions namely hyperbolic function solutions and trigonometric function solutions contain an explicit linear function of the variables in the considered equation it is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems

how far one can go with the exp function method a criterion determining if an exact solution of a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed in this paper this criterion is based on the concept of ranks of hankel matrixes constructed from sequences of coefficients produced by symbolic multiplicative operator techniques the employment of this criterion also gives an answer on the structure of the solution several examples are used to illustrate this concept

analytical solutions for nonlinear long short wave interaction systems with highly complex structure abstract in this paper we investigate and use the new modified exp expansion method mem we apply the new mem to nonlinear long short wave interaction systems nlswis among our findings are sets of solutions including but not limited to new hyperbolic complex and dark soliton solutions not only is mem shown to be highly adaptable for partial differential equations with strong nonlinearities but also it turns out to be highly efficient despite its ease

random sorting networks local statistics via random matrix laws this paper finds the bulk local limit of the swap process of uniformly random sorting networks the limit object is defined through a deterministic procedure a local version of the edelman greene algorithm applied to a two dimensional determinantal point process with explicit kernel the latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric gaussian unitary ensemble in particular the limiting law of the first time a given swap appears in a random sorting network is identified with the limiting distribution of the closest to 0 eigenvalue in the antisymmetric gue moreover the asymptotic gap in the bulk between appearances of a given swap is the gaudin mehta law the limiting universal distribution for gaps between eigenvalues of real symmetric random matrices the proofs rely on the determinantal structure and a double contour integral representation for the kernel of random poissonized young tableaux of arbitrary shape

exp function method for traveling wave solutions of nonlinear evolution equations in this paper we apply the exp function method to construct generalized solitary and periodic solutions of nonlinear evolution equations the proposed technique is tested on the modified zakharov kuznetsov zk and zakharov kuznetsov modified equal width zk mew equations these equations play a very important role in mathematical physics and engineering sciences the suggested algorithm is quite efficient and is practically well suited for use in these problems numerical results clearly indicate the reliability and efficiency of the proposed exp function method

the travelling wave solutions for non linear initial value problems using the homotopy perturbation method in this article we have used the homotopy perturbation method hpm to find the travelling wave solutions for some non linear initial value problems in the mathematical physics these problems consist of the burgers fisher equation the kuramoto sivashinsky equation the coupled schordinger kdv equations and the long short wave resonance equations together with initial conditions the results of these problems reveal that the hpm is very powerful effective convenient and quite accurate to the systems of non linear equations it is predicted that this method can be found widely applicable in engineering and physics

invariants of a family of scalar second order ordinary differential equations the family of second order equations with cubic nonlinearity in the first order derivative is closed with respect to an arbitrary point change of variables algebraic and differential invariants for these equations which depend on the first order derivatives are considered we solve completely the equivalence problem for this family of equations in the generic case and also for degenerate types of these equations fifty equations having the painleve property which have been classified by painleve and gambier belong to this remarkable family algebraic invariants of all these equations are calculated and constant invariants are listed in the paper invariant characterization of the fourth painleve equation is given

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

exact solutions of the drinfel d sokolov wilson equation using the exp function method abstract the generalized solitary solutions of the classical drinfel d sokolov wilson equation dswe are obtained using the exp function method then some of these solutions are easily converted into kink shaped solutions and blow up solutions by a simple transformation

a generalized expansion method for nonlinear wave equations a generalized jacobian exponential expansion method for finding the exact traveling wave solutions of a nonlinear partial differential equation is discussed we use this method to construct many new previously undiscovered exact solutions for the boussinesq and modified kdv equations we also apply it to the shallow long wave approximate equations new solutions are deduced for this system of partial differential equations

the first integral method for the time fractional kaup boussinesq system with time dependent coefficient the first integral method fim is applied to reach the different type solutions of the time fractional kaup boussinesq fkb system with time dependent coefficient it is obtained the envelope bell shaped triangular and kink soliton solutions of this equation the method is an effective one to reach the different types of solutions of fractional nonlinear partial differential equations fnpde

an exp function method for new n soliton solutions with arbitrary functions of a 2 1 dimensional vcbk system in this paper the exp function method is generalized to construct n soliton solutions of the 2 1 dimensional variable coefficient broer kaup vcbk system as a result new and more general 1 soliton 2 soliton and 3 soliton solutions with arbitrary functions are obtained from which the uniform formulae of n soliton solutions are derived based on one of the obtained 2 soliton solution the fission and fusion phenomena between the peakons and solitary waves are investigated it is shown that the exp function method may provide us with a straightforward effective and alternative mathematical tool for generating n soliton solutions of nonlinear evolution equations in mathematical physics

a generalized g g expansion method and its application to the 2 1 dimensional broer kaup equations abstract in this paper a generalized g g expansion method is used to seek more general exact solutions of the 2 1 dimensional broer kaup equations as a result non travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions trigonometric function solutions and rational solutions the proposed method is more powerful than wang et al s method in m l wang x z li j l zhang the g g expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics phys lett a 372 2008 417 423 and it can be used for many other nonlinear evolution equations in mathematical physics

comments on a new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the exp function method in their recent manuscript lei zhao et al claim that they have constructed an algorithm for automatic construction of solitary wave solutions to nonlinear partial differential equations based on the exp function method we argue that this algorithm does inherit all problems associated to the exp function method we show that this algorithm produces solutions which do not satisfy the original differential equation even if the solutions would be correct the exp function method would not be able to determine necessary and sufficient conditions for the existence of solitary solutions in the space of initial conditions and parameters

n soliton solutions of the kp equation by exp function method abstract in this paper the exp function method is generalized to determine the 1 soliton 2 soliton and 3 soliton solutions of the kadomtsev petviashvili kp equation then the uniform formula of n soliton solutions is derived the method is simple and straightforward in constructing the n soliton of the nonlinear evolution equation in mathematical physics

the oriented swap process particles labelled 1 n are initially arranged in increasing order subsequently each pair of neighboring particles that is currently in increasing order swaps according to a poisson process of rate 1 we analyze the asymptotic behavior of this process as n oo we prove that the space time trajectories of individual particles converge when suitably scaled to a certain family of random curves with two points of non differentiability and that the permutation matrix at a given time converges to a certain deterministic measure with absolutely continuous and singular parts the absorbing state where all particles are in decreasing order is reached at time 2 o 1 n the finishing times of individual particles converge to deterministic limits with fluctuations asymptotically governed by the tracy widom distribution

special solutions of the toda chain and combinatorial numbers we classify all solutions of the restricted toda chain from the ansatz that all moments are expressed in terms of polynomials of some variable we show that each such solution corresponds to the sheffer class orthogonal polynomials it is shown that corresponding hankel determinants are related to some well known combinatorial numbers

application of exp function method for 3 1 dimensional nonlinear evolution equations in this paper the exp function method is used to construct solitary and periodic solutions of nonlinear partial differential equations we choose an example which includes kadomstev petviashvili equation and potantial ytsf equation to illustrate the method the method is straightforward and concise and its applications are promising the exp function method presents a wider applicability for handling nonlinear wave equations

exact solutions to the double sinh gordon equation by the tanh method and a variable separated ode method new exact travelling wave solutions for the double sinh gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ode method the painleve property v e u is employed to support the tanh method in deriving exact solutions the work emphasizes the power of the methods in providing distinct solutions of different physical structures

an improvement on the exp function method when balancing the highest order linear and nonlinear terms abstract the exp function method has been widely used to solve different kinds of nonlinear partial differential equations these nonlinear partial differential equations are transformed first into nonlinear ordinary differential equations and then the ansatz of the exp function method u n c p a n exp n m d q b m exp m is applied to obtain the solution however a part of the solution using this method is to construct the relations between c p d and q by balancing the highest order linear term with the highest order nonlinear term it is proved in the present paper that c d and p q are the only relations that can be obtained by applying this method to any nonlinear ordinary differential equation therefore the additional calculations of balancing the highest order linear term with the highest order nonlinear term are not longer required in future hence the method becomes more straightforward

new abundant solutions for the burgers equation this paper applies a new modified exp function method to search for exact solitary solutions of the burgers equation using the imaginary transformation suggested by he and wu solitary solutions can be easily converted into periodic or compacton like solutions many new solutions are appearing for the first time in the open literature

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

a variational principle for coupled nonlinear schrodinger equations with variable coefficients and high nonlinearity via he s semi inverse method a variational principle is established for coupled nonlinear schrodinger equations with variable coefficients and high nonlinearity the result obtained includes the ones known from the open literature as special cases

discrete semi classical orthogonal polynomials generalized charlier abstract generalized charlier polynomials are introduced as semi classical orthogonal polynomials of class 1 with one parameter main characteristic data are established from the laguerre freud equations generating the coefficients of the recurrence relation satisfied by the polynomials