共查询到20条相似文献,搜索用时 375 毫秒
1.
该文基于对非稳定非线性薛定愕方程作反散射变换得到的Zakharov-Shabat方程,直接对积分核作变换,导出马尔钦科方程.得到的马尔钦科方程在形式上与一般非线性薛定谔方程得到的一样简单明了,且不存在逆变换的自洽困难. 相似文献
2.
一类非线性波动方程的显式精确解 总被引:14,自引:0,他引:14
本文用直接方法和假设的一种结合求出了一类较广泛的非线性波动方程utt-a1uxx+a2ut+a3u+a4uS^2+a5u^3=0的一些显式精确行波解,贱个有重要的非线性数学物理方程,如φ^4方程,Klein-Gordon方程,Sine-Gordon方程,及Sinh-Gordon方程的近似,Landau-Ginzburg-Higgs方程,Duffing方程,非线性电报方程等都可作为该方程的特殊情形得 相似文献
3.
Two types of symmetry reductions are derived for the variable coefficient MKdV equation, which contain well-known Painleve II type equation and Jacobian elliptic equation. In addition, soliton-like solutions of the variable coefficient MKdV equation are also obtained. Finally, a transformation between the variable coefficient MKdV equation and the MKdV equation are also found. 相似文献
4.
We derive a new four-dimensional partial differential equation with the isospectral Lax representation by shrinking the symmetry algebra of the reduced quasi-classical self-dual Yang–Mills equation and applying the technique of twisted extensions to the obtained Lie algebra. Then we find a recursion operator for symmetries of the new equation and construct a Bäcklund transformation between this equation and the four-dimensional Martínez Alonso–Shabat equation. Finally, we construct extensions of the integrable hierarchies associated to the hyper-CR equation for Einstein–Weyl structures, the reduced quasi-classical self-dual Yang–Mills equation, the four-dimensional universal hierarchy equation, and the four-dimensional Martínez Alonso–Shabat equation. 相似文献
5.
从牛顿运动方程出发,推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示,三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到,表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径. 相似文献
6.
Anwar Ja’afar Mohamad Jawad Anjan Biswas 《Applied mathematics and computation》2010,216(11):3370-3377
This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV-Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 相似文献
7.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(3):584-592
The tanh method and the extended tanh method are used for handling the Zhiber–Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd–Bullough–Mikhailov (DBM) equation, and Tzitzeica–Dodd–Bullough equation. Travelling wave solutions of different physical structures are formally derived for each equation. 相似文献
8.
从牛顿运动方程出发,推导了完整系统关于广义加速度的Lagrange方程.讨论了该方程与传统分析力学中的Lagrange方程的相容性问题.结果显示,三阶Lagrange方程可以通过对Lagrange方程求一阶时间导数得到,表明它们是相容的.因此三阶Lagrange方程提供了一种不同于传统Lagrange方程方法的求解物体运动方程的途径. 相似文献
9.
周之虎 《数学的实践与认识》2004,34(3):134-147
就 Mikusinski算符演算在方程求解方面的研究进展情况和已获得的重要结果作一综述 ,其内容有常系数线性微分方程、差分方程的 M算符解法 ;变数算符概念及其相关结果 ;变系数线性常微分方程、差分方程、差分微分方程的 M算符解法以及 M算符演算在其他方程求解中的应用 . 相似文献
10.
We derive infinitely many conservation laws for some multidimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schrödinger equation, modified lattice Boussinesq equation, Hietarinta’s Boussinesq-type equations, Schwarzian lattice Boussinesq equation, and Toda-modified lattice Boussinesq equation. 相似文献
11.
A demonstration of how the point symmetries of the Chazy equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy equation under a generalized transformation, and find the point symmetries of the Chazy equation are generalized symmetries for the new equation. With the use of singularity analysis and a simple coordinate transformation we construct a solution for the Chazy equation which is given by a right Painlevé series. The singularity analysis is applied to the new third-order equation and we find that it admits two solutions, one given by a left Painlevé series and one given by a right Painlevé series where the leading-order behaviors and the resonances are explicitly those of the Chazy equation. 相似文献
12.
In this paper we investigate mappings of the classical Fitzhugh–Nagumo equation to a generalized Fitzhugh–Nagumo equation. These mappings are invertible and transform the solutions of the classical Fitzhugh–Nagumo equation into solutions of the generalized Fitzhugh–Nagumo equation considered here. These mappings are found by considering the Lie point symmetries admitted by the classical Fitzhugh–Nagumo equation and the generalized Fitzhugh–Nagumo equation considered here. A particular example of a generalized Fitzhugh–Nagumo equation that satisfies the boundary conditions of the classical Fitzhugh–Nagumo equation is considered. Numerical solutions of the generalized Fitzhugh–Nagumo equation that do not satisfy the boundary conditions of the classical Fitzhugh–Nagumo equation are obtained by implementing the Method of Lines. 相似文献
13.
本文建立了非线性Boltzmann输运方程与线性AKNS方程之间的直接联系,从而以不同于Chapman,Enskog和Grad的方式,使Boltzmann方程化归为Dirac方程的求解。在没有其他外场作用的情形中,Boltzmann方程的精确解可以用逆散射方法来求得。 相似文献
14.
Mohamed Hayek 《Applied mathematics and computation》2011,218(6):2407-2420
Based on the simplest equation method, we propose exact and traveling-wave solutions for a nonlinear convection-diffusion-reaction equation with power law nonlinearity. Such equation can be considered as a generalization of the Fisher equation and other well-known convection-diffusion-reaction equations. Two important cases are considered. The case of density-independent diffusion and the case of density-dependent diffusion. When the parameters of the equation are constant, the Bernoulli equation is used as the simplest equation. This leads to new traveling-wave solutions. Moreover, some wavefront solutions can be derived from the traveling-wave ones. The case of time-dependent velocity in the convection term is studied also. We derive exact solutions of the equations by using the Riccati equation as simplest equation. The exact and traveling-wave solutions presented in this paper can be used to explain many biological and physical phenomena. 相似文献
15.
张卫国 《应用数学与计算数学学报》1994,(2)
首先求出了Lienard方程的显式精确解,进而求出了Rangwala-Rao方程,Ablowitz方程,Chen-Lee-Lin方程,以及Gerdjikov-Ivanov方程的型如的显式精确孤波解。 相似文献
16.
结合对偶变量理论,为压电热弹性体混合层合板问题推导了齐次的控制方程和Hamilton等参元列式.首先根据广义的Hamilton变分原理推导了压电热弹性体非齐次的Hamilton正则方程.然后进一步考虑了热平衡方程与导热方程中变量的对偶关系,通过增加正则方程的维数,成功地将非齐次的正则方程转化为能独立求解压电热弹性体耦合问题的齐次控制方程.为了推导四节点Hamilton等参元列式的方便,可将温度梯度关系类比成本构关系并构建新的变分原理.齐次方程大大简化了人们在分析压电热弹性体耦合问题时,通常要求解非齐次方程和关于平衡方程和导热方程的二阶微分方程的繁琐方法,同时也减少了数值计算工作量. 相似文献
17.
Abdul-Majid Wazwaz 《Applied mathematics and computation》2010,217(5):2277-2281
In this work we study the KdV equation and the Gardner equation with time-dependent coefficients and forcing term for each equation. A generalized wave transformation is used to convert each equation to a homogeneous equation. The soliton ansatz will be applied to the homogeneous equations to obtain soliton solutions. 相似文献
18.
The Self-similar Solution for Ginzburg-Landau Equation and Its Limit Behavior in Besov Spaces
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Xiaoyi Zhang 《偏微分方程(英文版)》2003,16(4):361-375
In this paper, we study the limit behavior of self-similar solutions for the Complex Ginzburg-Landau (CGL) equation in the nonstandard function space E_{s,p}. We prove the uniform existence of the solutions for the CGL equation and its limit equation in E_{s,p}. Moreover we show that the self-similar solutions of CGL equation converge, globally in time, to those of its limit equation as the parameters tend to zero. Key Words Ginzburg-Landau equation; Schrödinger equation; self-similar solution; limit behavior. 相似文献
19.
Jan Dereziński 《Annales Henri Poincare》2014,15(8):1569-1653
The paper is devoted to a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F 1 equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, recurrence relations of their solutions, their integral representations and discrete symmetries are discussed. 相似文献
20.
Lijun Zhang Jianming Zhang Yuzhen Bai Robert Hakl 《Journal of Applied Analysis & Computation》2019,9(5):1987-1998
The singular traveling wave solutions of a general 4-parameter family equation which unifies the Camass-Holm equation, the Degasperis-Procesi equation and the Novikov equation are investigated in this paper. At first, we obtain the explicit peakon solutions for one of its specific case that $a=(p+2)c$, $b=(p+1)c$ and $c=1$, which is referred to a generalized Camassa-Holm-Novikov (CHN) equation, by reducing it to a second-order ordinary differential equation (ODE) and solving its associated first-order integrable ODE. By observing the characteristics of peakon solutions to the CHN equation, we construct the peakon solutions for the general 4-parameter breaking wave equation. It reveals that singularities of the peakon solutions come up only when the solutions attain singular points of the equation, which might be a universal principal for all singular traveling wave solutions for wave breaking equations. 相似文献