共查询到19条相似文献,搜索用时 187 毫秒
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应用进一步修正的简单方程法对修正的 Benjamin -Bona -Mahoney (mBBM )方程进行求解,给出了mBBM方程新的精确类孤波解,取定某些参数值,便可得到精确孤波解.这种方法也可用于寻找其它常系数以及变系数非线性发展方程(组)的精确解,具有一定的普适性. 相似文献
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张哲李德生 《原子与分子物理学报》2013,(5):829-832
应用进一步修正的简单方程法对修正的Benjamin-Bona-Mahoney(mBBM)方程进行求解,给出了mBBM方程新的精确类孤波解,取定某些参数值,便可得到精确孤波解.这种方法也可用于寻找其它常系数以及变系数非线性发展方程(组)的精确解,具有一定的普适性. 相似文献
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A quite general coupled variable coefficient modified
KdV (VCmKdV) equation in a two-layer fluid system is derived by
means of the reductive perturbation method. Making use of the CK's
direct method, some similarity reductions of the coupled VCmKdV equation
are obtained and their corresponding group explanations are discussed.
Some exact solutions of the coupled equations are also presented. 相似文献
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根据尖峰孤子解的特点,提出了一种待定系数法求非线性波方程尖峰孤子解的思路和方法,并利用该方法求解了5个非线性波方程,即CH(Camassa-Holm)方程、五阶KdV-like 方程、广义Ostrovsky方程、组合KdV-mKdV方程和Klein-Gordon方程,比较简便地得到了这些方程的尖峰孤子解.文献中关于CH方程的结果成为本文结果的特例.通过数值模拟给出了部分解的图像.简要说明了非线性波方程存在尖峰孤子解所须满足的特定条件.该方法也适用于求其他非线性波方程的尖峰孤子解.
关键词:
非线性波方程
尖峰孤子解
待定系数法 相似文献
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New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm 总被引:1,自引:0,他引:1
YAN Zhen-Ya 《理论物理通讯》2004,42(11)
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the correspondingsystem of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献
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YANZhen-Ya 《理论物理通讯》2004,42(5):645-648
A Weierstrass elliptic function expansion method and its algorithm are developed in this paper. The method changes the problem solving nonlinear evolution equations into another one solving the corresponding system of nonlinear algebraic equations. With the aid of symbolic computation (e.g. Maple), the method is applied to the combined KdV-mKdV equation and (2 1)-dimensional coupled Davey-Stewartson equation. As a consequence, many new types of doubly periodic solutions are obtained in terms of the Weierstrass elliptic function. Jacobi elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions. 相似文献
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Using the relation between the mKdV equation and the KdV-mKdV equation, we derive non-singular rational solutions for the mKdV equation. The solutions are given in terms of Wronskians. Dynamics of some solutions is investigated by means of asymptotic analysis. Wave trajectories of high order rational solutions are asymptotically governed by cubic curves. 相似文献
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MA Zheng-Yi 《理论物理通讯》2007,48(2):199-204
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the (2+1)-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations. 相似文献
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MA Zheng-Yi 《理论物理通讯》2007,48(8):199-204
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations. As concrete examples of its application, we apply this method to the (2 1)-dimensional modified Broer-Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations. 相似文献
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New Travelling Wave Solutions to Compound KdV-Burgers Equation 总被引:1,自引:0,他引:1
The compound KdV-Burgers equation and combined KdV-mKdV equation
are real physical models concerning many branches in
physics. In this paper, applying the improved trigonometric function
method to these equations, rich explicit and exact travelling
wave solutions, which contain solitary-wave solutions, periodic
solutions, and combined formal solitary-wave solutions, are
obtained. 相似文献