(2+1)维Kadomtsev-Petviashvili方程的留数对称及其相互作用解

运用Painlevé截断展开方法得到(2+1)维Kadomtsev-Petviashvili(KP)方程的非局域留数对称和B?cklund变换.由于非局域对称不能直接对(2+1)维KP方程进行约化求解,因此,需要将非局域对称局域化.然后,利用相容的Riccati展开(CRE)可解的概念证明(2+1)维KP方程的CRE可解性,从而求出(2+1)维KP方程的新的相互作用解.     

(2+1)维Boussinesq方程的呼吸波解

应用Hirota双线形形式和拓展同宿测试法研究了一类(2+1)维Boussinesq方程的性质,借助Maple计算软件,获得了方程的新的双波解和呼吸孤立波解.     

(2+1)-维广义Benney-Luke方程的精确行波解

用平面动力系统方法研究(2+1)-维广义Benney-Luke方程的精确行波解,获得了该方程的扭波解,不可数无穷多光滑周期波解和某些无界行波解的精确的参数表达式,以及上述解存在的参数条件．     

(3+1)维extended Jimbo-Miwa方程的精确解

应用Hirota双线性方法和新三波测试函数研究了(3+1)维extend JimboMiwa方程,借助Maple计算软件,获得了12组它的精确解.通过选取适当的参数,做出一部分精确解的图形来说明他们的物理特征.     

2+1 维变系数广义KP方程的椭圆周期解

运用Jacobi椭圆函数展开法求得了2 1维变系数广义KadoratsevPetviashvili方程的椭圆周期解及孤立波解．     

（2＋1）维KP方程的三类精确解

研究了（2＋1）维KP方程的孤子解问题．应用Riccati方程映射法,得到了（2＋1）维KP方程的新的显式精确解的结构．根据得到的精确解结构,构造出了该方程的三类精确解．     

指数型一次Logistic迭代方程解的周期倍分岔现象

本文讨论了指数型一次Ｌｏｇｉｓｔｉｃ迭代方程解的周期倍分岔现象的存在性,给出了周期倍分合时的临界点参数应满足的方程,并证明了周期倍分岔的临界点参数序列的极限是存在的,进而证明了当参数越过这个极限时,指数型一次 Ｌｏｇｉｓｔｉｃ迭代方程存在混沌解．     

低维宏观交通流模型的稳定性和分岔分析

交通流模型的分岔点对应临界的交通状态,对研究交通流的稳定性具有重要的理论意义.为了分析宏观交通流模型的分岔特征,通过对低维宏观交通流模型的求解得到两个平衡点,并讨论了其稳定性,发现该模型存在一个跨临界分岔点.数值仿真验证了结论的正确性,并且在一定条件下,通过改变响应时间会影响到最终的平衡状态.     

(2+1)维浅水波方程的新精确解

对(2+1)维浅水波方程的现有解进行了推广.应用CK方法对方程进行求解,得到方程的Backlund变换公式,将已知解代入公式,求得一些新的精确解,从而推广了浅水渡方程的解.     

2+1-维变系数广义Kadomtsev-Petviashvili方程的相似约化

借助于MATHEMATICA软件,将直接约化法推广并应用到2+1-维变系数广义Kadomtsev-Petviashvili(VCGKP)方程,获得了VCGKP方程的若干相似约化,其中包括PainleveⅠ型、PainleveⅡ型和PainleveⅣ型的约化.     

(2+1)维破裂孤子方程及Kadomtsev-Petviashvili方程的Stable-range解法(英文)

By using Xu’s stable-range method,families of explicit exact solutions with multiple parameter functions for the(2+1)-dimensional breaking soliton and KadomtsevPetviashvili equations.These parameter functions make our solutions more applicable to related practical models and boundary value problems.     

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.     

Peakon Soliton Solutions Of K(2,-2,4) Equation

In this paper, the qualitative analysis methods of a dynamical system are used to investigate the peakon soliton solutions of K(2;-2; 4) equation: ut + a(u2)x + b[u-2(u4)xx]x = 0. The phase portrait bifurcation of the traveling wave system corresponding to the equation is given. The explicit expressions of the peakon soliton solutions are obtained by using the portraits. The graph of the solutions are given with the numerical simulation. This supplements the results obtained in [4].     

(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.     

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.     

Lump solutions to the generalized (2+1)-dimensional B-type Kadomtsev-Petviashvili equation

Through symbolic computation with Maple, the (2+1)-dimensional B-type Kadomtsev-Petviashvili(BKP) equation is considered. The generalized bilinear form not the Hirota bilinear method is the starting point in the computation process in this paper. The resulting lump solutions contain six free parameters, four of which satisfy two determinant conditions to guarantee the analyticity and rational localization of the solutions, while the others are arbitrary. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters.     

(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.     

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.