(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解和高阶怪波解

基于Hirota双线性方法,利用拓展的同宿呼吸检验法得到了(3+1)维变系数Kudryashov-Sinelshchikov(K-S)方程的同宿呼吸波解,对该解的参数选取合适的数值,可得到不同结构的同宿呼吸波.通过对同宿呼吸波解的周期取极限,推导出方程的怪波解.最后,构造出一个特殊的高阶多项式作为测试函数,求得该方程的一阶怪波解和二阶怪波解.     

一个2+1维变形Boussinesq方程的N孤子解

研究了一个2＋1维变形Boussinesq非线性发展方程：utt-uxx-uyy-3（u^2）xx-uxxxx=0,运用Hirota双线性方法得到它的N孤子解.     

Wick型随机(2+1)维mZK方程的精确解

随机分析和白噪声理论的建立和发展为浅水波方程的研究提供了新的内容,方法和工具.本文研究随机环境下(2+1)维mZK方程的精确解问题.在Kondratiev分布空间(y)-1中利用Hermite变换和改进的Fan代数方法,得到Wick型随机(2+1)维mZK方程和变系数(2+1)维mZK方程的白噪声泛函解和精确解.     

Lump and mixed rogue-soliton solutions to the 2+1 dimensional Ablowitz-Kaup-Newell-Segur equation

In this paper, the 2+1 dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation which obtained from the potential Boiti-Leon-Manna-Pempi nelli (pBLMP) equation, is introduced. Through the bilinear method and ansatz technique, the rational solutions consisting of rogue wave and lump soliton solutions are constructed, where we discuss the condition of guaranteeing the positiveness and analyticity of the lump solutions. The collection of a quadratic function with an exponential function describing rational-exponential solutions is proved, the interaction consisting of one lump and one soliton with fission and fusion phenomena. The second kind of interaction comprises the line rogue wave and soliton solution, which is inelastic. With the usage of the extended homoclinic test approach, the homoclinic breather-wave solution is derived. The characteristics of these various solutions are exhibited and illustrated graphically.     

Determinant Solutions Generalized KP Equation to a （3＋1）-Dimensional with Variable Coefficients

A system of linear conditions is presented for Wronskian and Grammian solutions to a (3+1)-dimensional generalized vcKP equation.The formulations of these solutions require a constraint on variable coefficients.     

Hirota-Satsuma方程的N-孤子解(英文)

In this work,using the Hirota bilinear method,N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation:u_t - u_xxt - 3u_xu_t + u_x = 0.     

Jacobi Elliptic Function Solutions and Traveling Wave Solutions of the (2 + 1)-Dimensional Gardner-KP Equation

The fully integrable KP equation is one of the models that describes the evolution of nonlinear waves, the expansion of the well-known KdV equation, where the impacts of surface tension and viscosity are negligible. This paper uses the Modified Extended Direct Algebraic (MEDA) method to build fresh exact, periodic, trigonometric, hyperbolic, rational, triangular and soliton alternatives for the (2 + 1)-dimensional Gardner KP equation. These solutions that we discover in this article will help us understand the phenomena of the (2 + 1)-dimensional Gardner KP equation. Comparing the study in this paper and existing work, we find more exact solutions with soliton and periodic structures and the rational function solution in this paper is more general than the rational solution in existing literature. Most of the Jacobi elliptic function solutions and the mixed Jacobi elliptic function solutions to the (2 + 1)-dimensional Gardner KP equation discovered in this paper, to the best of our highest understanding are not seen in any existing paper until now.     

用改进的代数方法构造(2+1)维ZK-MEW方程的精确行波解

利用一种改进的统一代数方法将构造(2+1)维ZK MEW((2+1)-dimensionalZakharov-Kuznetsovmodifiedequalwidth)方程精确行波解的问题转化为求解一组非线性的代数方程组．再借助于符号计算系统Mathematica求解所得到的非线性代数方程组,最终获得了方程的多种形式的精确行波解．其中包括有理解,三角函数解,双曲函数解,双周期Jacobi椭圆函数解,双周期Weierstrass椭圆形式解等．并给出了部分解的图形.     

Multiple rogue wave solutions for a (3+1)-dimensional Hirota bilinear equation

In this paper, we considered the multiple rogue wave solutions of a (3+1)-dimensional Hirota bilinear equation by using a symbolic computation approach. Based on the bilinear form of this equation, the first-order rogue waves, the second-order rogue waves and the third-order rogue waves are presented. Moreover, some basic properties of multiple rogue waves and their collision structures are explained by drawing the three dimensional plot.     

SOLITON SOLUTIONS TO AN EQUATION IN 2+1 DIMENSIONS

This paper considers a 2+1 dimensional equation. A bilinear form for the equation and its 3-soliton solutions are obtained by the Hirota method. The N-soliton solution is given in the form of pfaffian. At the same time the proof of the solutions are given.     

(2+1)维Burgers方程新的复合解

In this paper, a new generalized compound Riccati equations rational expansion method （GCRERE） is proposed. Compared with most existing rational expansion methods and other sophisticated methods, the proposed method is not only recover some known solutions, but also find some new and general complexiton solutions. Being concise and straightforward, it is applied to the （2＋1）-dimensional Burgers equation. As a result, eight families of new exact analytical solutions for this equation are found. The method can also be applied to other nonlinear partial differential equations.     

任意方程法及BKP方程新的精确解

In this paper,auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation.We study the(2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions.The method used here can be also extended to other nonlinear partial differential equations.     

(2+1)-维破裂孤子方程的群叶状方法和显式解

利用等变活动标架理论,研究(2+1)-维破裂孤子方程的群叶状方法和显式解.原方程的对称群的无穷维部分被用来产生整个解空间的叶状结构,于是分解系统就继承了对称群的有限维部分.求解的过程完全符号化和算法化.利用群叶状方法,破裂孤子方程的一些显式精确解被得到,这些解关于无穷维对称子群封闭.     

Extended tanh-function Metho d for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, by using the balancing method and the extended tanh-function method, we obtain the exact traveling wave solutions of Kundu equation with fifth-order nonlinear term. Applications of this method to some other nonlinear partial differential equations are also presented.     

Asymptotic behavior of the periodic wave solution for the (3+1)-dimensional Kadomtsev-Petviashvili equation

In this paper, the one- and two-periodic wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation are presented by means of the Hirota’s bilinear method and the Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure.     

Extend three-wave method for the (1+2)-dimensional Ito equation

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.     

2+1维Ginzburg-Landau方程的精确波解

分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解.     

具任意次非线性项的Camassa-Holm方程的双孤子新解

给出辅助方程、函数变换与变量分离解相结合的方法,构造了具任意次非线性项的Camassa-Holm方程的双孤子和双周期新解.首先,通过两个辅助方程、函数变换与变量分离解,将具任意次非线性项的Camassa-Holm方程的求解问题转化为非线性代数方程的求解问题.然后,借助符号计算系统Mathematica求出该方程组的解,并用辅助方程的相关结论,构造了双周期解和双孤子新解.     

A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions

We aim to explore new (2+1)-dimensional nonlinear equations which possess lump solutions. Through the Hirota bilinear method, we formulate a combined fourth-order nonlinear equation while guaranteeing the existence of lump solutions. The class of lump solutions is constructed explicitly in terms of the coefficients of the combined nonlinear equation via symbolic computations. Specific examples are discussed to show the richness of the considered combined nonlinear equation. Three dimensional plots and contour plots of specific lump solutions to two specially chosen cases of the equation are made to shed light on the presented lump solutions.