CH-γ方程的多孤子解

利用Darboux变换得到CH-γ方程的多孤子解, 其中一些解的性质与CH方程的不同.     

ON COMPLETE INTEGRABILITY OF A HIERARCHY OF FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

A hierarchy of Hamiltonian systems obtained from the Lax pair of KdV hierarchy under theconstraint condition on potential u = (q, q) is. presented. The independent integrals for theseHamiltonian systems are constructed by using recursion operator and shown to be in involution.Thus this hierarchy of Hamiltonian systems is completely integrable in the sense of Liouville. andthey commute with each other.     

Zakharov-Shabat 特征值问题及 AKNS 型发展方程的非线性迭加公式

在非线性发展方程中，为了由方程的已知解求出它的另一些解，给出这些方程的Bcklund变换以及由此而导出的非线性迭加公式是一个十分重要的方法。目前已有不     

关于简支的Reissner厚板的自由振动

§1.在数学物理及工程技术中,关于经典薄板的振动问题已经进行过大量的讨论与计算。但是有关考虑横向剪切影响的Reissner厚板的振动问题,讨论得不多。我们在某大坝的抗震计算中遇到了这类问题。     

THE DARBOUX-TRANSFORMATION METHOD FOR FINDING THE SOLUTIONS OF A SYSTEM OF NONLINEAR KLEINGORDON EQUATIONS

§1. Introduction Recently, the author has successfully used the Darboux-transformations' method for finding the solutions of some classes of nonlinear evolution equations which are associated with 2×2 eigenvalue problems. In this paper, we extend this method for finding the solutions     

Exact Solutions of （2＋1）-Dimensional Euler Equation Found by Weak Darboux Transformation

The weak Darboux transformation of the （2＋1） dimensional Euler equation is used to find its exact solutions. Starting from a constant velocity field solution, a set of quite general periodic wave solutions such as the Rossby waves can be simply obtained from the weak Darboux transformation with zero spectral parameters. The constant vorticity seed solution is utilized to generate Bessel waves.     

Bäcklund变换的递推算子之间的转换算子I

本文首先通过引入递推算子之间的转换算子,证明了两类Bäcklund交换是等价变换及相应的两类发展方程是等价方程;其次利用特征值问题存在的规范变换,得到了这些方程的无穷守恒律的密度和流的关系;最后借助一个新的泛函求导公式,从一类发展方程的Hamilton形式导出另一类发展方程的Hamilton形式。     

A HIERARCHY OF INTEGRABLE HAMILTONIAN SYSTEMS WITH NEUMANN TYPE CONSTRAINT

A hierarchy of integrable Hamiltonian systems with Neumann type constraint isobtained by restricting a hierarchy of evolution equations associated with λφ_(xx)+u_iλ~iφ=λ~mφ to aninvariant subspace of their recursion operator.The independentintegrals of motion and Hamiltonian functions for these Hamiltonian systems areconstructed by using relevant reeursion formula and are shown to be in involution.Thusthese Hamiltonian systems are completely integrable and commute with each other.     

关于简支厚板与薄板的关系

厚板的数学理论是建立在与薄板不同的力学假定的基础上的。本文分析了厚板与薄板之间静力学方面的关系。对于任意的简支多边形板,得到了厚板解通过薄板解的显式表达式,从而证明了:Reissner模型的厚板解与薄板解具有相同的剪力,但弯矩、转角、挠度有差别;而washizu模型的厚板解则与薄板解不仅剪力相同,连弯矩与转角亦相同,只是挠度有差别。