共查询到19条相似文献,搜索用时 281 毫秒
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本文利用奇异摄动的理论和方法,研究v2?4μ时KdVB方程的行波解,得到行波解的三阶渐近展开式的显式,同时得到行波解的一般渐近展开式的表达式:u≈u(0)+εu(1)+ε1u(2)+…+εnu(n)+…;并且证明u(j)(j=1,2,…,n,…)都是有界函数。
关键词: 相似文献
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本文研究了推广的KdV方程 ut+2μuux+v3x+δu5x=0(μvδ≠0) (1)的精确孤子解,得到了(1)式的一些新的孤波解,对文献[10]的若干结论作了补充与修正。
关键词: 相似文献
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Cheng-Shi Liu 《Foundations of Physics》2011,41(5):793-804
To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties
with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling
wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As
a result, we prove that the Burgers-KdV equation does not have the real solution in the form a
0+a
1tan ξ+a
2tan 2
ξ, which indicates that some types of the solutions to the Burgers-KdV equation are very limited, that is, there exists no
new solution to the Burgers-KdV equation if the degree of the corresponding polynomial increases. For the second equation,
we obtain some new solutions. In particular, some interesting structures in those solutions maybe imply some physical meanings.
Finally, we discuss some classifications of the reaction-diffusion equations which can be solved by trial equation method. 相似文献
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To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations. 相似文献
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By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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HUANGDing-Jiang ZHANGHong-Qing 《理论物理通讯》2004,42(2):171-174
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UUτyy ? UyUτy + U2Uτ + 3Uy = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations of the smooth and nonsmooth soliton solutions for the Novikov equation with cubic nonlinearity. These solutions contain peaked soliton, smooth soliton, W-shaped soliton and periodic solutions. Our work extends some previous results. 相似文献
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In this paper, we find exact solutions of some nonlinear evolution equations by using generalized tanh–coth method. Three nonlinear models of physical significance, i.e. the Cahn–Hilliard equation, the Allen–Cahn equation and the steady-state equation with a cubic nonlinearity are considered and their exact solutions are obtained. From the general solutions, other well-known results are also derived. Also in this paper, we shall compare the generalized tanh–coth method and generalized (G ′/G )-expansion method to solve partial differential equations (PDEs) and ordinary differential equations (ODEs). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important roles in engineering fields. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized tanh–coth method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems. 相似文献
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By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
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Based on the Lax triple (Bm, Bn, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions. 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