共查询到19条相似文献,搜索用时 203 毫秒
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将试探方程法应用到变系数非线性发展方程的精确解的求解.以两类变系数KdV方程为例,在相当一般的参数条件下求得了丰富的精确解,其中包括新解.
关键词:
试探方程法
变系数KdV方程
类椭圆正弦(余弦)波解
类孤子解 相似文献
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本文为了获得非线性发展方程的无穷序列新精确解,进一步研究获得了第二种椭圆方程的几类新型解和Bäcklund变换.在此基础上,借助符号计算系统Mathematica,用带强迫项变系数组合KdV方程、(2+1)维和(3+1)维变系数Zakharov-Kuznetsov 方程为应用实例,构造了无穷序列新精确解.这里包括无穷序列Jacobi 椭圆函数光滑孤立子解、无穷序列Jacobi椭圆函数紧孤立子解、无穷序列三角函数紧孤立子解和无穷序列尖峰孤立子解.
关键词:
第二种椭圆方程
Bä
cklund 变换
变系数非线性发展方程
无穷序列新精确解 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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Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation 下载免费PDF全文
By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions. 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
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利用映射方法和一个适当的变换,得到大量的有弱偏置磁场及含时激光场中的非线性Gross-Pitaevskii方程的新解,这些解包括椭圆函数解,椭圆函数叠加解,三角函数解,亮孤子解,暗孤子解和类孤子解。 相似文献