广义KdV方程的若干新的精确解

本文利用守恒律方程等价的概念和求精确解的方法,对广义KdV方程求出了若干新解。     

A geometric characterization of the nonlinear Schr?dinger equation and its applications

We prove that the nonlinear Schr?dinger equation of attractive type (NLS⁺) describes just spherical surfaces (SS) and the nonlinear Schr?dinger equation of repulsive type (NLS^-) determines only pseudospherical surfaces (PSS). This implies that, though we show that given two differential PSS (resp. SS) equations there exists a local gauge transformation (despite of changing the independent variables or not) which transforms a solution of one into any solution of the other, it is impossible to have such a gauge transformation between the NLS⁺ and the NLS^-.     

A geometric characterization of the nonlinear Schrödinger equation and its applications

Science China Mathematics - We prove that the nonlinear Schrödinger equation of attractive type (NLS+) describes just spherical surfaces (SS) and the nonlinear Schrödinger equation of...     

A semidiscrete Gardner equation

We construct the Darboux transformations, exact solutions, and infinite number of conservation laws for a semidiscrete Gardner equation. A special class of solutions of the semidiscrete equation, called table-top solitons, are given. The dynamical properties of these solutions are also discussed.