共查询到16条相似文献,搜索用时 125 毫秒
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无阻尼单摆运动微分方程是一种具有物理背景的非线性常微分方程,研究其精确解和解法是非线性科学中的一个重要内容.在F展开法的基础上,应用反正切分式变换正弦函数方法,并引入Riccati辅助方程,得到了4种无阻尼单摆方程精确解的结果.达到了丰富此类方程求解技巧和精确解的目的.总结得出此类方程应用反正切分式变换方法具有一定普适性的结论. 相似文献
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为了获得非线性差分微分方程的无穷序列精确解,引入一种双曲函数型辅助方程,并给出该方程解的Bcklund变换和解的非线性叠加公式.在此基础上,利用辅助方程与函数变换相结合的方法,借助符号计算系统Mathematica,用一般格子方程为应用实例,获得了无穷序列精确解。 相似文献
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This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics. 相似文献
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本文为了构造非线性发展方程的无穷序列尖峰精确解,给出了Riccati方程的Bäcklund 变换和解的非线性叠加公式,并借助符号计算系统Mathematica,用Degasperis-Procesi方程为应用实例,构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解.
关键词:
Riccati方程
解的非线性叠加公式
尖峰孤立波解
Degasperis-Procesi 方程 相似文献
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New exact solitary wave solutions to generalized mKdV equation and generalized Zakharov--Kuzentsov equation 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper,
based on hyperbolic tanh-function method and homogeneous balance
method, and auxiliary equation method, some new exact solitary
solutions to the generalized mKdV equation and generalized
Zakharov--Kuzentsov equation are constructed by the method of
auxiliary equation with function transformation with aid of
symbolic computation system Mathematica. The method is of important
significance in seeking new exact solutions to the evolution
equation with arbitrary nonlinear term. 相似文献
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The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term 总被引:3,自引:0,他引:3 下载免费PDF全文
By use of an auxiliary equation and through a function transformation, the Jacobi
elliptic function wave-like solutions, the degenerated soliton-like solutions and
the triangle function wave solutions to two kinds of Korteweg--de Vries (KdV)
equations with variable coefficients and a KdV equation with a forcible term are
constructed with the help of symbolic computation system Mathematica, where the new
solutions are also constructed. 相似文献