一维Tonks-Girardeau原子气区域中 Gross-Pitaevskii方程简化模型的精确行波解

利用动力系统方法研究一维Tonks-Girardeau原子气区域中Gross-Pitaevskii (GP)方程简化模型的一些精确行波解以及这些精确行波解的动力学行为, 研究系统的参数对行波解的动力学行为的影响. 在不同的参数条件下, 获得了一维Tonks-Girardeau原子气区域中GP方程简化模型的六个行波解的精确参数表达式. 关键词： 动力系统方法 孤立波解 周期波解 扭波解     

(2+1)维扰动时滞破裂孤波方程行波解的摄动方法

研究了一类(2+1)维扰动时滞破裂孤波方程. 首先讨论了对应的无时滞情形下的破裂方程,利用待定系数投射方法得到了孤波精确解. 再利用同伦、摄动近似方法得到了扰动破裂孤波方程的行波渐近解. 关键词： 孤波 行波解 近似解     

Hybrid-Lattice系统和Ablowitz-Ladik-Lattice系统的新解探索

对tanh函数方法进行了对称延拓，并拓广了它的应用范围，将其应用于非线性离散系统的求解.研究了Hybrid Lattice系统和Ablowitz Ladik Lattice系统.得到了方程的孤波解和周期波解. 关键词： 改进的tanh函数方法 离散系统 孤波解 周期波解     

非线性波动方程的Jacobi椭圆函数包络周期解

应用Jacobi椭圆函数展开法求得了一类非线性波方程的包络周期解,而且用这种方法得到的周期解在一定条件下可以退化为包络冲击波解或包络孤立波解 关键词： Jacobi椭圆函数 非线性方程 包络周期解 包络孤立波解     

(2+1)维广义Nizhnik-Novikov-Veselov系统的新严格解和复合波激发

利用拓展的Riccati方程映射法与变量分离法，得到了(2+1)维广义Nizhnik-Novikov-Veselov(GNNV)系统新的含有两个任意函数的相当广义的变量分离严格解.根据其中的周期波解，找到了该系统的复合波，即在周期波背景下的孤立波，并简要讨论了其演化行为. 关键词： GNNV系统 拓展Riccati映射 周期波解 孤立波     

扩展的双曲函数法和Zakharov方程组的新精确孤立波解

借助于符号计算软件Maple，利用扩展的双曲函数法求出了Zakharov方程组的精确孤立波解，包括钟状孤立波解、扭结状孤立波解、包络孤立波解、奇性孤立波解和一种新的形式的孤立波解.这种方法也适用于其他非线性波方程.     

Jacobi椭圆函数展开法及其在求解非线性波动方程中的应用

给出了Jacobi椭圆函数展开法,且应用该方法获得了几种非线性波方程的准确周期解.该方法包含了双曲函数展开法,应用该方法得到的周期解包含了冲击波解和孤波解. 关键词： Jacobi椭圆函数 非线性方程 周期解 孤波解     

长短波相互作用方程的Jacobi椭圆函数求解

推广了Jacobi椭圆函数展开方法,研究了复非线性演化方程组的求解问题,得到了长短波相互作用方程的准确包络周期解.该结果在一定条件下包含了相应的孤波解. 关键词： Jacobi椭圆函数方法 长短波相互作用方程 孤波解     

有流存在时三层流体界面波的二阶Stokes波解

以小振幅波理论为基础，利用摄动方法研究了有背景流场存在时密度三层成层状态下的界面内波，得到了各层流体速度势的二阶渐近解及界面内波波面位移的二阶Stokes波解，并讨论了界面波的Kelvin-Helmholtz不稳定性.结果表明：有流存在的情况下三层密度成层流体界面内波的一阶渐近解(线性波解)、频散关系及二阶渐近解不仅依赖于各层流体的厚度和密度，也依赖于各层流体的背景流场；界面内波波面位移的二阶Stokes波解不仅描述了界面波之间的二阶非线性相互作用，也描述了背景流与界面波之间的二阶非线性相互作用；当每层流 关键词： 界面波 均匀流 二阶Stokes波解 Kelvin-Helmholtz不稳定性     

KdV型方程孤波解与KdV-Burgers型方程行波解的稳定性

证明了KdV型议程的孤波解和KdV-Burgers型方程的行波解在李亚诺夫意义下是不是稳定的，从而修正了文献中的一些结论。     

Applications of the first integral method to nonlinear evolution equations

<正>In this paper,we establish travelling wave solutions for some nonlinear evolution equations.The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations.The obtained results include periodic and solitary wave solutions.The first integral method presents a wider applicability to handling nonlinear wave equations.     

Extended F-Expansion Method and Periodic Wave Solutionsfor Klein-Gordon-Schrödinger Equations

We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrödinger equations are obtained. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained.     

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.     

New exact travelling wave solutions of the generalized zakharov equations

A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained.     

Bosonized Supersymmetric Sawada–Kotera Equations: Symmetries and Exact Solutions

The Bosonized Supersymmetric Sawada–Kotera(BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada–Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out.     

Linear superposition solutions to nonlinear wave equations

The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed.     

A procedure to construct exact solutions of nonlinear evolution equations

In this paper, we implemented the functional variable method for the exact solutions of the Zakharov?CKuznetsov-modified equal-width (ZK-MEW), the modified Benjamin?CBona?CMahony (mBBM) and the modified KdV?CKadomtsev?CPetviashvili (KdV?CKP) equations. By using this scheme, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. The functional variable method presents a wider applicability for handling nonlinear wave equations.     

Bifurcations and new exact travelling wave solutions for the bidirectional wave equations

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of Maple software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional wave equations. The results presented in this paper improve the related previous studies.     

修正cKdV方程组的孤立波结构及其稳定性

利用函数展开法求解修正耦合KdV(Coupled KdV,cKdV)方程组,得到几类孤立波解,包括扭结型-钟型、双扭结型、双钟型以及双扭结-双钟型结构的单孤子解.在不同的极限情况下,这些解分别退化为修正cKdV方程的扭结状或钟状孤波解.对孤立波的稳定性进行了数值研究,结果表明:修正cKdV方程既存在稳定的孤立波解,也存在不稳定的孤立波解.     

New solitons and periodic wave solutions for the dispersive long wave equations

We make use of Jacobi elliptic functions to construct periodic wave solutions for the dispersive long wave equations. In the limit cases the multiple soliton solutions are also obtained. The properties of some periodic and soliton solutions for the dispersive long wave equations are shown by some figures. As a result, we can successfully obtain the solitary wave solutions that can be found by the previous work.