共查询到19条相似文献,搜索用时 78 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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根据变系数modified Korteweg-de Vries(VCmKdV)方程与常系数KdV-mKdV方程的非线性项、色散项的相似性,对解已知的KdV-mKdV方程做适当变换,并将它的解移植到解未知的VCmKdV方程,由此构造出两个不同方程解之间的移植关系.利用这种解的移植方法,求得了由两层流体模型经演化获得的含有源(或汇)耦合VCmKdV系统新的精确解和类孤波解.对Bcklund变换与解的移植法进行了比较,分析了源和汇对波幅的影响.
关键词:
解的移植法
KdV-mKdV方程
耦合VCmKdV系统
类孤波解 相似文献
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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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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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利用一种推广的代数方法,求解了一类广义Boussinesq方程(B(m,n)方程)和Boussinesq-Burgers方程(B-B方程).获得了其多种形式的显式精确解,包括孤波解、三角函数解、有理函数解、Jacobi椭圆函数周期解和Weierstrass椭圆函数周期解,进一步丰富了这两类方程的解.
关键词:
Boussinesq方程
Boussinesq-Burgers方程
推广的代数方法
显式精确解 相似文献
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A new method of new exact solutions and solitary wave-like solutions for the generalized variable coefficients Kadomtsev-Petviashvili equation 总被引:1,自引:0,他引:1 下载免费PDF全文
Using the solution of general Korteweg-de Vries (KdV) equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili (KP) equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained. 相似文献
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Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili (vKP) equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation. 相似文献
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For a variable coefficient Kadomtsev-Petviashvili (KP) equation the Lax pair as well as conjugate Lax pair are derived from the Painleve analysis.The N-fold binary Darboux transformation is presented in a compact form.As an application,the multi-lump,higher-order lump and general lump-soliton interaction solutions for the variable coefficient KP equation are obtained.Typical lump structures with amplitudes exponentially decaying to zero as the time tends to infinity and interactions between one lump and one soliton are shown. 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(2):323-336
A new type of the nonisospectral KP equation with self-consistent sources is constructed by using the source generation procedure. A new feature of the obtained nonisospectral system is that we allow y-dependence of the arbitrary constants in the determinantal solution for the nonisospectral KP equation. In order to further show integrability of the novel nonisospectral KP equation with self-consistent sources, we give a bilinear Bäcklund transformation. 相似文献
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This paper constructs more general exact solutions than N-soliton solution and Wronskian solution for variable- coefficient Kadomtsev-Petviashvili (KP) equation. By using the Hirota method and Pfaffian technique, it finds the Grammian determinant-type solution for the variable-coefficient KP equation (VCKP), the Wronski-type Pfaffian solution and the Gram-type Pfaffian solutions for the Pfaffianized VCKP equation. 相似文献
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New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional KP equation with variable coefficients 下载免费PDF全文
A new generalized Jacobi elliptic function method is used to construct the exact travelling wave solutions of nonlinear partial differential equations (PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation which has more new solutions. More new doubly periodic and multiple soliton solutions are obtained for the generalized (3+1)-dimensional Kronig-Penny (KP) equation with variable coefficients. This method can be applied to other equations with variable coefficients. 相似文献
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高娃 《原子与分子物理学报》2005,22(4):757-761
利用埃尔米特变换和特殊的截断展开法求出(2+1)-维Wick类型随机广义KP方程的类孤子解. 这种方法的基本思想是通过埃尔米特变换把(2+1)-维Wick类型随机广义KP方程变成的(2+1)-维广义变系数KP方程,利用特殊的截断展开方法求出方程的解,然后通过埃尔米特的逆变换求出方程的随机解. 相似文献
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A simple algebraic transformation relation of a special type of solution between the (3 1)-dimensional Kadomtsev-petviashvili(KP) equation and the cubic nonlinear Klein-Gordon equation (NKG) is established.Using known solutions of the NKG equation,we can obtain many soliton solutions and periodic solution of the (3 1)-dimensional KP equation. 相似文献
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In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a (1+1)- dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili (KP) equation are obtained. 相似文献