共查询到19条相似文献,搜索用时 62 毫秒
1.
由loop代数的一个子代数出发,构造了一个线性等谱问题,再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构,作为该可积系统的约化,得到了著名的Schrdinger方程和mKdV方程,因此称该系统为S-mKdV方程族.根据已构造的的子代数,又构造了维数为5的loop代数的一个新的子代数,由此出发设计了一个线性等谱形式,再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例,求得了著名的Schrdinger方程和mKdV方程的可积耦合系统. 相似文献
2.
3.
梁金福 《原子与分子物理学报》2010,27(5):921-926
本文利用一种该进的映射法和线性变量分离法,得到(2+1)-维色散长波方程大量的,带有两个任意函数的精确解。并在得到的一个周期波精确解的基础上,通过选择恰当的函数,可以观察到(2+1)-维色散长波方程的折叠孤立波的演化行为。 相似文献
4.
5.
研究一类广义非线性Schrordinger方程的孤立子解及其性质,研究非线性参数变化时孤立子性态的变化规律,同时研究该系统的数值解法,得到了一类广义非线性Schroedinger方程差分格式的收敛性和稳定性的条件。 相似文献
6.
7.
8.
9.
10.
量子多体问题或量子场论中有一类模型是可以精确求解的,这类模型称作量子可积模型.量子可积模型的主要特征是:系统的守恒量数目与系统自由度的数目相同(对于具有无限自由度的系统,守恒量的数目亦为无限),从而使系统的本征态、本征能谱及热力学量都可精确求得.自从1931年Bethe~[1]首次求得一维Heisenberg链的精确解后,许多一维量子多体物理模型或(1+1)维(一维空间加一维时间)量子场论模型都获得了精确解.这些精确解曾对于人们理解许多物理现象(如稀磁合金中的Kondo效应)起到了极为重要的作用.如何将这方面的理论推广到高维空间,即寻找并精… 相似文献
11.
采用分步确定拟解的原则, 对齐次平衡法求非线性发展方程孤子解的关键步骤作了进一步改 进. 以广义Boussinesq方程和bidirectional Kaup-Kupershmidt方程为应用实例, 说明使用 该方法可有效避免“中间表达式膨胀”的问题, 除获得标准Hirota形式的孤子解外, 还能获 得其他形式的孤子解.
关键词:
齐次平衡法
孤子解
孤波解
广义Boussinesq方程
bidirectional Kaup-Kupershmi dt方程 相似文献
12.
13.
The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed. 相似文献
14.
Variational iteration method is implemented to construct solitary solutions for nonlinear dispersive equations. In this scheme the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Many models are approached and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions. 相似文献
15.
Three important nonlinear evolution equations are solved with the aid of the symbolic manipulation system.Maple,using the direct algebraic method proposed recently,We explicitly obtain several new solutions of physical interest in addition to rederiving all the known solutions. 相似文献
16.
17.
Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV–mKdV equation are chosen to illustrate the effectiveness of the method. 相似文献
18.
Some new solitary and travelling wave solutions of certain nonlinear diffusion-reaction equations using auxiliary equation method 总被引:1,自引:0,他引:1
Attempts are made to look for the soliton content in the exact solutions of certain types of nonlinear diffusion-reaction (DR) equations with the quadratic and cubic nonlinearities. Such equations may arise in a variety of contexts in physical problems. In this Letter using the auxiliary equation method, some new solitary and travelling wave solutions of such nonlinear DR equations are obtained in a very general form. Several interesting special cases of these general solutions are also discussed. 相似文献
19.
A review of the generic features as well as the exact analytical solutions of a class of coupled scalar field equations governing nonlinear wave modulations in dispersive media like plasmas is presented. The equations are derivable from a Hamiltonian function which, in most cases, has the unusual property that the associated kinetic energy is not positive definite. To start with, a simplified derivation of the nonlinear Schrödinger equation for the coupling of an amplitude modulated high-frequency wave to a suitable low-frequency wave is discussed. Coupled sets of time-evolution equations like the Zakharov system, the Schrödinger-Boussinesq system and the Schrödinger-Korteweg-de Vries system are then introduced. For stationary propagation of the coupled waves, the latter two systems yield a generic system of a pair of coupled, ordinary differential equations with many free parameters. Different classes of exact analytical solutions of the generic system of equations are then reviewed. A comparison between the various sets of governing equations as well as between their exact analytical solutions is presented. Parameter regimes for the existence of different types of localized solutions are also discussed. The generic system of equations has a Hamiltonian structure, and is closely related to the well-known Hénon-Heiles system which has been extensively studied in the field of nonlinear dynamics. In fact, the associated generic Hamiltonian is identically the same as the generalized Hénon-Heiles Hamiltonian for the case of coupled waves in a magnetized plasma with negative group dispersion. When the group dispersion is positive, there exists a novel Hamiltonian which is structurally same as the generalized Hénon-Heiles Hamiltonian but with indefinite kinetic energy. The above correspondence between the two systems has been exploited to obtain the parameter regimes for the complete integrability of the coupled waves. There exists a direct one-to-one correspondence between the known integrable cases of the generic Hamiltonian and the stationary Hamiltonian flows associated with the only integrable nonlinear evolution equations (of polynomial and autonomous type) with a scale-weight of seven. The relevance of the generic system to other equations like the self-dual Yang-Mills equations, the complex Korteweg-de Vries equation and the complexified classical dynamical equations has also been discussed. 相似文献