THE MODIFIED HELMHOLTZ EQUATIONS AND THEIR BOUNDARY VALUE PROBLEMS

§1. Concept of a Generalized Holomorphic Vector In mathematical problems of space technics, nuclear technics, laser and electron technics, we often encounter many boundary value problems (BVPs) of Modified Helmholtz Equations (MHEs), so how to solve these equations attracts our attention.     

非线性波动方程类五大特色的内在联系

我们利用K-dv方程阐明非线性波动方程类五大特色:1)逆散射方法、2)Bäcklund变换、3)、守恒律、4)N-孤立子解、5)完全可积Hamilton系统之间的内在联系。     

THE NECESSARY CONDITION FOR SHORT RANGE SOLITON SOLUTION OF GKdV EQUATION

In this note, the necessary condition for short range soliton solution of generalized Koteweg de Vries (GKdV) equation is found out and proved by means of the Pontryagine's maximum principle.     

THE CAUCHY INTEGRAL OF MANY COMPLEX VARIABLES PASSIVE OPERATORS AND MULTIDIMENSIONAL DISPERSION RELATIONS

This note illustrates the multidimensional dispersion relations that connect the realand imaginary parts of the matrix z(p):where(?)(p)is the boundary value of the impedance(?)(ζ).     

FREDHOLM DETERMINANT SOLUTION FOR NONLINEAR EQUATIONS ASSOCIATED WITH ISOSPECTRAL SCHRODINGER EICENVALUE PROBLEM

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广义BOLTZMANN方程的可解性（1）

在研究气体动力学的冲击波、激光核聚变及离子发动机的过程中会遇到一类非线性的积分微分方程(一般提法)     

THE EXISTENCE AND UNIQUENESS THEOREMS OF THE LINEAR AND NONLINEAR RIEMANNHILBERT PROBLEMS FOR THE GENERALIZED HOLOMORPHIC VECTOR OF THE SECOND KIND

务1.The Generalized Holomorphic Vector and itsFundamental Theore们。s The linear and nonlinear Ri“mann一Hilber七problem,(RHP)for七he generaliz喊holomorPhio veotor(GHV)of七he oecond klnd are imPortan七boundary valueProblemsw址oliof七en姗ur in mathematioal problemg OfSP姗俪h川os,nuolear七印hni田,l叻er and eleo七ron teohnioS[,一51,七hat are al的ex七remely diffioul七proble叫to be solved.However,七he印eoialo朋e of th田e Problems haveb旧ens七ndy in ourpreoedlng paPer〔1,.The RHP for七he h…     

多复变Cauchy积分和被动算子与多重色散关系

本文阐述多重色散关系联系着矩阵z(p)的实部与虚部:,式中z(p)是阻抗z(ζ)的边值.