Exact Periodic-Wave Solutions for （2＋1）-Dimensional Boussinesq Equation and（3＋1）-Dimensional KP Equation

The (2 1)-dimensional Boussinesq equation and (3 1)-dimensional KP equation are studied by using the extended Jacobi elliptic-function method. The exact periodic-wave solutions for the two equations are obtained.     

Variable Separation Solutions in (1+1)-Dimensional and (3+1)-Dimensional Systems via Entangled Mapping Approach

In this paper, the entangled mapping approach (EMA) is applied to obtain variable separation solutions of (1 1)-dimensional and (3 1)-dimensional systems. By analysis, we firstly find that there also exists a common formula to describe suitable physical fields or potentials for these (1 1)-dimensional models such as coupled integrable dispersionless (CID) and shallow water wave equations. Moreover, we find that the variable separation solution of the (3 1)-dimensional Burgers system satisfies the completely same form as the universal quantity U1 in (2 1 )-dimensional systems. The only difference is that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables.     

Exact Solutions to (2+1)-Dimensional Kaup--Kupershmidt Equation

In this paper, by using the symmetry method, the relationships between new explicit solutions and old ones of the (2+1)-dimensional Kaup-Kupershmidt (KK) equation are presented. We successfully obtain more general exact travelling wave solutions for (2+1)-dimensional KK equation by the symmetry method and the (G^, /G)-expansion 　method. Consequently, we find some new solutions of (2+1)-dimensional KK equation, 　including similarity solutions, solitary wave solutions, and 　periodic solutions.     

Exact Solutions of (2+1)-Dimensional HNLS Equation

In this paper, we use the classical Lie group symmetry method to get the Lie point symmetries of the (2+1)-dimensional hyperbolic nonlinear Schrödinger (HNLS) equation and reduce the (2+1)-dimensional HNLS equation to some (1+1)-dimensional partial differential systems. Finally, many exact travelling solutions of the (2+1)-dimensional HNLS equation are obtained by the classical Lie symmetry reduced method.     

Multisymplectic Pseudospectral Discretizations for (3+1)-Dimensional Klein-Gordon Equation

We explore the multisymplectic Fourier pseudospectral discretizations for the (3+1)-dimensional Klein-Gordon equation in this paper. The corresponding multisymplectic conservation laws are derived. Two kinds of explicit symplectic integrators in time are also presented.     

New Exact Solution to (3+1)-Dimensional Burgers Equation

In this Letter, using Backlund transformation and the new variable separation approach, we find a new general solution to the (3 1)-dimensional Burgers equation. The form of the universal formula obtained from many (2 1)-dimensional systems is extended. Abundant localized coherent structures can be found by seclecting corresponding functions appropriately.     

New Soliton-like Solutions for (2+1)-Dimensional Breaking Soliton Equation

The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method.     

Folded Localized Excitations of the (2 + 1)-Dimensional Broer-Kaup Equation

Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.     

New Exact Solution to （3＋1）-Dimensional Burgers Equation

In this Letter, using Ba^ecklund transformation and the new variable separation approach, we find a new general solution to the (3 1)-dimensional Burgers equation. The form of the universal formula obtained from many (2 1)-dimensional systems is extended. Abundant localized coherent structures can be found by seclecting corresponding functions appropriately.     

Variable Separation Solution for （1＋1）-Dimensional Nonlinear Models Related to Schroedinger Equation

A variable separation approach is proposed and successfully extended to the (1 1)-dimensional physics models. The new exact solution of (1 1)-dimensional nonlinear models related to Schr6dinger equation by the entrance of three arbitrary functions is obtained. Some special types of soliton wave solutions such as multi-soliton wave solution,non-stable soliton solution, oscillating soliton solution, and periodic soliton solutions are discussed by selecting the arbitrary functions appropriately.     

Folded Localized Excitations of the （2＋1）-Dimensional Broer-Kaup Equation

Considering that the multi-valued (folded) localized excitations may appear in many (2 1)-dimensional soliton equations because some arbitrary functions can be included in the exact solutions, we use some special types of muliti-valued functions to construct folded solitrary waves and foldons in the (2 1)-dimensional Broer-Kaup equation.These folded excitations are invesigated both analytically and graphically in an alternative way.     

Abundant Multisoliton Structure of the (3+1)-Dimensional Nizhnik-Novikov-Veselov Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation. By means of the leading order term analysis, the nonlinear transformations of the (3+1)-dimensional NNV equation are given first, and then some special types of single solitary wave solution and the multisoliton solutions are constructed.     

Integrability and Solutions of the (2+1)-Dimensional Broer-Kaup Equation with Variable Coefficients

The integrability of the (2+1)-dimensional Broer-Kaup equation with variable coefficients (VCBK) is verified by finding a transformation mapping it to the usual (2+1)-dimensional Broer-Kaup equation (BK). Thus the solutions of the (2+1)-dimensional VCBK are obtained by making full use of the known solutions of the usual (2+1)-dimensional BK. Two new integrable models are given by this transformation, their dromion-like solutions and rogue wave solutions are also obtained. Further, the velocity of the dromion-like solutions can be designed and the center of the rogue wave solutions can be controlled artificially because of the appearance of the four arbitrary functions in the transformation.     

New Compacton-Like and Solitary Pattern-Like Solutions of (2+1)-Dimensional Generalization of Modified KdV Equation

Recently some (1 1)-dimensional nonlinear wave equations with linearly dispersive terms were shown to possess compacton-like and solitary pattern-like solutions. In this paper, with the aid of Maple, new solutions of (2 1)-dimensional generalization of mKd V equation, which is of only linearly dispersive terms, are investigated using three new transformations. As a consequence, it is shown that this (2 1)-dimensional equation also possesses new compacton-like solutions and solitary pattern-like solutions.     

New Exact Solutions for (2+1)-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breaking soliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutions and triangular periodic wave solutions are obtained.     

Conformal Invariant Asymptotic Expansion Approach for Solving (3+1)-Dimensional JM Equation

The (3+1)-dimensional Jimbo-Miwa (JM) equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new (3+1)-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.     

New Exact Solutions and Conservation Laws to (3+1)-Dimensional Potential-YTSF Equation

Using the modified CK's direct method, we build the relationship between new solutions and old ones and find some new exact solutions to the (3+1)-dimensional potential-YTSF equation. Based on the invariant group theory, Lie point symmetry groups and Lie symmetries of the (3+1)-dimensional potential-YTSF equation are obtained. We also get conservation laws of the equation with the given Lie symmetry.     

Applications of Extended Mapping Deformation Method in Two (3+1)-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.     

A New (2+1)-Dimensional KdV Equation and Its Localized Structures

A new (2+1)-dimensional KdV equation is constructed by using Lax pair generating technique. Exact solutions of the new equation are studied by means of the singular manifold method. Bäcklund transformation in terms ofthe singular manifold is obtained. And localized structures are also investigated.     

Fission and Fusion of Solitons for the （1＋1）—Dimensional Kupershmidt Equation

By means of the heat conduction equation and the standard truncated Painleve expansion,the (1 1)-dimensional Kupershmidt equation is solved.Some significant exact multi-soliton solutions are given.Especially,for the interaction of the multi-solitons of the Kupershmidt equation,we find that a single(resonant)kink or bell soliton may be fissioned to several kink or bell solitons,Inversely,several kink or bell solitons may also be fused to one kink or bell soliton.