广义双曲函数法求解(2+1)维变系数Nizhnik-Novikov-Veselov方程新的孤子解

非线性现象在数学、物理学、生物学、大气动力学、生命科学等自然科学领域中频频被发现,这些非线性问题基本上都可以用非线性发展方程来描述。本文为获得非线性发展方程的孤子解,借助符号计算软件Mathematical,研究了广义双曲函数方法,并应用广义双曲函数法获得了(2+1)维变系数Nizhnik-Novikov-Veselov方程新的孤子解。

(2+1)维变系数Nizhnik-Novikov-Veselov方程的孤子解

孤立子的高度稳定性和粒子性引起了人们对孤立子的极大兴趣,并且在流体物理、固体物理、等离子体物理和光学实验中频频被发现,很多非线性发展方程都存在孤立子解。本文在符号计算的帮助下,利用一个广义的双曲函数方法,得到(2+1)维变系数Nizhnik-Novikov-Veselov方程的新的更广义类型的孤子解,此方法还可被应用到其它非线性发展方程中去。

New Multiple Soliton-like and Periodic Solutions for （2＋l）-Dimensional Canonical Generalized KP Equation with Variable Coefficients

In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.

Symbolic Computation and New Families of Exact Non-travelling Wave Solutions of （2＋1）-dimensional Broer-Kaup Equations

The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.

Traveling Wave Solutions for Generalized Bretherton Equation

This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He＇s semi-inverse method （He＇s variational method）. Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.