EQUATION OF MATHEMATICAL PHYSICS AND OTHER AREAS OF APPLICATION: A CLASSICAL INTEGRABLE SYSTEM AND THE INVOLUTIVE REPRESENTATION OF SOLUTIONS OF THE HIGHER ORDER KAUP-NEWELL EQUATION

Under the constrained condition induced by the eigenfunction expresson of the potential (u, v)T = (-[A2q, q], [A2p, p])T = f (q, p), the spatial part of the Lax pair of the Kaup-Newell equation is non linearized to be a completely integrable system (R2N, Adp AND dq, H = H-1) with the Hamiltonian H-1 = -[A3q, p]-1/2[A2p, p][A2q, q]. while the nonlinearization of the time part leads to its N-involutive system {H(m)}. The involutive solution of the compatible fsystem (H-1), (H(m)) is mapped by into the solution of the higher order Kaup-Newell equation.

THE COMPLETELY INTEGRABLE SYSTEMS OF THE COMPLEX FORM AND THE COUPLED AKNS-KAUP-NEWELL EQUATION HIERARCHY

In this paper, the coupled AKNS-Kaup-Newell equation hierarchy are obtained by means of the new spectral problem. By means of the complex representation of the standard symplect form on R4N, and the constraint relations between the potential and the wave functions, the new completely integrable systems of the complex form are got. Therefore, the involutive solutions of the coupled AKNS-Kaup-Newell equation hierarchy are given.

高阶AKNS方程的对合解

本文在文献［１］的基础上，借助于可换流的对合解，给出高阶ＡＫＮＳ方程的对合解。

Harry—Dym方程的对合解

在位势与特征函数之间的一个代数约束下,Harry—Dym方程的Lax对被非线性化为两个相容的Hamilton系统。通过约束映射,它们的对合解产生Harry—Dym方程的有限带解与孤子解。

高阶色散水波方程的对合解(英文)

讨论了高阶色散水波方程的Lax对.在位势与特征函数之间的约束条件下,Lax系统被非线性化成为有限维Liouville完全可积系统.

一族孤子方程对应的C·Neumann系统

在位势与特征函数之间的约束下,谱问题y_(xx)=(λ^(-1)u+v+λW)y-λ~2y被非线性化为一个Liouville意义下的完全可积的C·Neumann系统。我们获得一个新的N对合系并且给出与这个谱问题相联系的孤子方程族的对合解。

Abel范畴中线性态射方程的公共解及一类同解方程

给出了Ａｂｅｌ范畴中形如φχψ＝τ的态射方程有解的充要条件以及线性态射方程φχ＝τ１，χψ＝τ２有公共解的条件。

一族非线性发展方程解的对合表示及所对应的对合守恒积分系

本文针对线性谱问题利用“非线性化”方法给出与之相应的一族非线性发展方程解的对合表示；并证明了文献［１］中节４中４）里的对合守恒积分系Ｆ＿ｍ：实际上是由该族方程Ｌａｘ表示的时间部分之非线性化而导致；另外，顺便还给出了一个驻定的非线性系统．

一族4×4AKNS方程的对合解

本文获得了一族ＡＫＮＳ方程及其Ｌａｘ表示．用文献［２］和［３］的方法证明了可以从两个方面相容的常微分方程组的相容解构造出４×４ＡＫＮＳ非线性偏微分方程的解。