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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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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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The generalized ZK–BBM equation is solved using iterative scheme of the Adomian decomposition method (ADM) and variational iteration method (VIM). A dark and a kink soliton solutions of the generalized ZK–BBM equation are obtained under initial conditions. The convergence analysis of the ADM and VIM solution shows that these solutions are convergent. The comparison of the ADM and VIM solutions with the exact solution shows that the solutions of the generalized ZK–BBM equation by the iterative methods are almost exact. The absolute errors show that the accuracy and efficiency of the ADM and VIM depend on the problem and its domain. It is found that the iterative scheme of Adomian decomposition method and variational iteration method are quite efficient for the soliton solution of the generalized ZK–BBM equation. 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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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