一类偏微分方程组的一般解及其在壳体理论中的应用

本文给出了构造一类偏微分方程组一般解的方法,用这种方法构造的一般解是完备的。最后,利用这个方法构造了壳体中的柱壳平衡方程和锥壳运动方程的一般解。     

SIMILARITY REDUCTIONS FOR THE NONLINEAR EVOLUTION EQUATION ARISING IN THE FERMI-PASTA-ULAM PROBLEM

ＩｎｔｒｏｄｕｃｔｉｏｎＦｅｒｍｉ,ＰａｓｔａａｎｄＵｌａｍ[1]ｐｒｅｓｅｎｔｅｄａｗｅｌｌ＿ｋｎｏｗｎｐｒｏｂｌｅｍｗｈｙｓｏｌｉｄｓｈａｄｆｉｎｉｔｅｈｅａｔｃｏｎｄｕｃｔｉｖｉｔｙ ,ｗｈｉｃｈｗａｓｃａｌｌｅｄｔｈｅＦｅｒｍｉ＿Ｐａｓｔａ＿Ｕｌａｍ(ＦＰＵ)ｐｒｏｂｌｅｍ .Ｔｈｅｓｏｌｉｄｉｓｍｏｄｅｌｌｅｄｂｙａｏｎｅ＿ｄｉｍｅｎｓｉｏｎａｌｌａｔｔｉｃｅ ,ａｓｅｔｏｆｍａｓｓｅｓｃｏｕｐｌｅｄｂｙｓｔｒｉｎｇ .Ｔｈｅｅｑｕａｔｉｏｎｓｇｏｖｅｒｎｉｎｇｔｈｅｄｙｎａｍｉｃｓｏｆｔｈｉｓｌａ…     

利用李代数构造非线性可积及双可积哈密顿耦合

With the help of a Lie algebra,two kinds of Lie algebras with the forms of blocks are introduced for generating nonlinear integrable and bi-integrable couplings.For illustrating the application of the Lie algebras,an integrable Hamiltonian system is obtained,from which some reduced evolution equations are presented.Finally,Hamiltonian structures of nonlinear integrable and bi-integrable couplings of the integrable Hamiltonian system are furnished by applying the variational identity.The approach presented in the paper can also provide nonlinear integrable and bi-integrable couplings of other integrable system.     

非线性发展方程的Wronskian解及Young图证明

给出一般非线性发展方程构造Wronskian解的间接法. 根据Young图运算的性质给出了文中命题的证明, 并讨论了置换群特征标与Young图表达式系数间的关系. 关键词： 非线性发展方程 Wronskian解 Young图 特征标     

一个新的Liouville可积系统及其Lax表示，Bi—Hamilton结构

从一个特征值问题出发,首先推导一族非线性发展方程,其中包括著名MKdV方程做为特殊约化,进一步证明这族方程在Liounille意义下可积并具有Bi-Hamilton结构,而在位执函数和特征函数之间的一定约束下,特征值问题被非线性化为一完全可积的有限维Hamilton系统。     

广义组合KdV-mKdV方程的显式精确解

Abstract. With the aid of Mathematica and Wu-elimination method,via using a new generalizedansatz and well-known Riccati equation,thirty-two families of explicit and exact solutions forthe generalized combined KdV and mKdV equation are obtained,which contain new solitarywave solutions and periodic wave solutions. This approach can also be applied to other nonlinearevolution equations.     

新的Lax可积发展方程族及其无限维双-哈密顿结构

基于一个新的具有三个位势函数(q,r,s)的等谱问题,获得了一族新的含有一个任意函数的Lax可积发展方程.特别地,当位势函数s取不同的函数时,这个方程族约化为若干类型的方程组,进一步利用迹恒等式,给出了这些方程组的双哈密顿结构,并且证明它们是Liouville可积的.此外,给出了守恒密度和对称. 关键词： 等谱问题 哈密顿结构 Lax可积 Liouville可积     

Lamé函数和非线性演化方程的新多级准确解

基于Lamé方程和新的Lamé函数,应用摄动方法和Jacobi椭圆函数展开法求解非线性演化方程,获得多种新的多级准确解.这些解在极限条件下可以退化为各种形武的孤波解.     

The Wronskian technique for nonlinear evolution equations

The investigation of the exact traveling wave solutions to the nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. To understand the mechanisms of those physical phenomena, it is necessary to explore their solutions and properties. The Wronskian technique is a powerful tool to construct multi-soliton solutions for many nonlinear evolution equations possessing Hirota bilinear forms. In the process of utilizing the Wronskian technique,the main difficulty lies in the construction of a system of linear differential conditions, which is not unique. In this paper,we give a universal method to construct a system of linear differential conditions.