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BBM方程和mKdV-ZK方程的新的精确周期解  [PDF]
张苗,张文亮,王军帽
安徽大学学报(自然科学版) , 2008,
Abstract:
一类新的可积系及其MKdV方程族  [PDF]
顾祝全
科学通报 , 1990,
Abstract: 寻求新的可积系是近年来孤子理论和可积系理论中的重要课题。本文研究一类新的孤子系统,给出其Lax表示,然后由该系统约化至著名的MKdV方程族,其Lax方程组经位势和特征函数的约束关系被非线性化为一有限维Liouville意义下的新的完全可积系的可换流,进而由可换流的对合解给出MKdV方程族的解的表示。
求解KdV方程和mKdV方程的新方法:(g'/g^2)展开法  [PDF]
王思源,陈浩
华南师范大学学报(自然科学版) , 2014,
Abstract: 根据(g'/g^2)展开法的相关原理和步骤,利用其求得KdV方程和mKdV方程的精确解.并在不同的情形下,得出三种通解双曲函数通解,三角函数通解及有理函数通解.双曲函数通解中相关参数取特殊值时,得出了孤立波解.从求解KdV方程和mKdV方程的过程可以得出,展(g'/g^2)开法与先前提出的(g'/g)展开法和其他方法具有简便,易于计算的特点,是求解非线性方程的较好选择.
A type of expanding integrable system for NLS-mKdV hierarchy
一类NLS-mKdV方程族的扩展可积系统

Zhang Yu-Feng,Yan Qing-You,
张玉峰
,闫庆友

物理学报 , 2003,
Abstract: 利用代数变换,构造了与文献[5]中的loop代数2的子代数等价的loop代数 1的一个子 代数1.再将1扩展为一个高维的loop代数.利用设计了一个等谱问题 ,结合子代数间的直 和运算和同构关系,得到了NLS_mKdV方程族的一类扩展可积系统.作为约化情形,求得了著 名的Schrdinger方程与mKdV方程的可积耦合系统.
A family of S-mKdV hierarchy of equations and its expanding integrable models
一类S-mKdV方程族及其扩展可积模型

Zhang Yu-Feng,Yan Qing-You,Zhang Hong-Qing,
张玉峰
,闫庆友,张鸿庆

物理学报 , 2003,
Abstract: 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Schrdinger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Schrdinger方程和mKdV方程的可积耦合系统.
mKdV Surfaces  [PDF]
Suleyman Tek
Mathematics , 2006, DOI: 10.1063/1.2409523
Abstract: In this work, we consider 2-surfaces in ${\mathbb R}^3$ arising from the modified Korteweg de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV equation. mKdV surfaces contain Willmore-like and Weingarten surfaces. We show that some mKdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial of the Gaussian and mean curvatures.
修正的简单方程法与sine-Godon方程和广义的变系数KdV-mKdV方程的精确解
The Modified Simple Equation Method and the Exact Solutions for the sine-Gordon Equation and the Generalized Variable-Coefficient KdV-mKdV Equation
 [PDF]

肖玲风, 斯仁道尔吉
Advances in Applied Mathematics (AAM) , 2016, DOI: 10.12677/AAM.2016.53055
Abstract: 本文用修正的简单方程法对sine-Gordon方程和广义的变系数KdV-mKdV方程进行求解,并给出了它们的行波解,当给参数取特殊值时,便可以得到相应的精确行波解。
The modified simple equation method is used to construct the exact solutions for the sine-Gordon equation and the generalized variable-coefficient KdV-mKdV equation. Some exact solutions of the hyperbolic function form for the sine-Gordon equation and the generalized variable-coefficient KdV-mKdV equation are derived by the method. When taking special values of the parameters, the exact traveling wave solutions of the equations are derived from the exact solutions.
CONSERVATION LAWS OF THE VARIABLE COEFFICIENT KdV AND MKdV EQUATIONS
变系数KdV方程和变系数MKdV方程的无穷多守恒律

LOU SEN-YUE,RUAN HANG-YU,
楼森岳
,阮航宇

物理学报 , 1992,
Abstract: In this paper, by using the Miura's method, we study the infinite conservation laws of the variable coefficient KdV and MKdV equations with three arbitrary functions of t. The result points out that the conserved densities which have the structures completely similar to the con-stat coefficient KdV and MKdV equations depend only on one arbitrary function. The other two arbitrary functions are contained only in the corresponding fluxes.
分子轨道的偏差分方程法  [PDF]
李向平
化学学报 , 1982,
Abstract: 本文在前文的基础上,提出求载波和能级的偏差分方程法.通过解偏差分方程的边值问题,求得几种分子轨道的能级公式和载波公式.
Improved tanh-function method and the new exact solutions for the general variab le coefficient KdV equation and MKdV equation
改进的tanh函数方法与广义变系数KdV和MKdV方程新的精确解

Li De Sheng,Zhang Hong Qing,
李德生
,张鸿庆

物理学报 , 2003,
Abstract: In this paper, by using the extended tanh-function method,the general variable coefficient KdV and MKdV equations are reduced to first-order variable coefficient nonlinear ordinary differential equations,and then the new exact solutions for these equations,which include exact soliton-like,rational formal and triangle function solutions,are obtained through solving these ordinary differential equations-
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