共查询到18条相似文献,搜索用时 93 毫秒
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提出了一种比较系统的求解非线性发展方程精确解的新方法, 即试探方程法. 以一个带5阶 导数项的非线性发展方程为例, 利用试探方程法化成初等积分形式,再利用三阶多项式的完 全判别系统求解,由此求得的精确解包括有理函数型解, 孤波解, 三角函数型周期解, 多项 式型Jacobi椭圆函数周期解和分式型Jacobi椭圆函数周期解
关键词:
试探方程法
非线性发展方程
孤波解
Jacobi椭圆函数
周期解 相似文献
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通过把十二个Jacobi椭圆函数分类成四组,提出了新的广泛的Jacobi椭圆函数展开法,利用这一方法求得了非线性发展方程的丰富的Jacobi椭圆函数双周期解.当模数m→0或1时,这些解退化为相应的三角函数解或孤立波解和冲击波解.
关键词:
非线性发展方程
Jacobi椭圆函数
双周期解
行波解 相似文献
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LIU Chun-Ping CHEN Jian-Kang CAI Fan 《理论物理通讯》2004,42(7)
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method. 相似文献
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LIUChun-Ping CHENJian-Kang CAIFan 《理论物理通讯》2004,42(1):74-78
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method. 相似文献
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We find a new family of fifth-order water-wave equations having common invariant manifold of the fourth order. These evolution equations are nonintegrable except for two cases corresponding to the Sawada–Kotera and Kaup–Kupershmidt equations. The invariant manifold of the family is an autonomous equation F-VI from the Cosgrove's classification of fourth-order ODEs having the Painlevé property. Two-parameter solutions of the equation F-VI allow to find two-soliton solutions for this family of evolution equations. 相似文献
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In terms of the solutions of an auxiliary ordinary differential
equation, a new algebraic method, which contains the terms of first-order
derivative of functions f(ξ), is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations. 相似文献
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In terms of the solutions of the generalized Riccati equation,
a new algebraic method, which contains the terms of radical expression of functions f(ξ), is constructed to explore
the new exact solutions for nonlinear evolution equations.
Being concise and straightforward, the method is applied to
nonlinear Klein-Gordon equation, and some new exact solutions
of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations. 相似文献
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辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解. 相似文献
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ZHI Hong-Yan ZHANG Hong-Qing 《理论物理通讯》2007,47(4):587-593
We combine the tanh function method with the symmetry group method to construct new type of solutions of Davey-Stewartson equation and implemente it in a computer algebraic system. As a result, some new types of solutions are obtained. This method is also applied to other differential equations if the nonlinear evolution equations admit nontrivial one-parameter group of transformation. 相似文献
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Complex Tanh-Function Expansion Method and Exact Solutions to Two Systems of Nonlinear Wave Equations 总被引:2,自引:0,他引:2
ZHANGJin-Liang WANGMing-Liang 《理论物理通讯》2004,42(4):491-493
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown. 相似文献