高阶非线性薛定谔方程的可积边界条件  

Integrable Boundary Conditions for Higher-order Nonlinear Schrodinger Equation

作　　者：王中园 张成 WANG Zhongyuan;ZHANG Cheng(Department of Mathematics,College of Science,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院数学系,上海200444

出　　处：《应用数学学报》2022年第5期673-686,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11875040,12171306)资助项目。

摘　　要：基于Sklyanin的可积边界理论,本文研究了二维可积聚焦非线性薛定谔方程族的可积边界条件.对于偶数阶非线性薛定谔方程,我们给出了一类可积边界条件;通过边界穿衣方法,我们构建了这一类方程在半直线上满足可积边界条件的多孤子解.对于定义在半直线上的奇数阶非线性薛定谔,可积边界方法只能得到该类方程的实退化:即所得方程退化为实方程.Based on Sklyanin’s formalism of integrable boundary,this paper studies integrable boundary conditions for the hierarchy of two-dimensional foucsing integrable nonlinear Schrodinger equations.We obtain,for even order nonlinear Schrodinger equations,a class of integrable boundary conditions;using the method of dressing the boundary,we construct soliton solutions of the equations on the half-line subject to integrable boundary conditions.As to half-line problems for odd order nonlinear Schrodinger equations,the formalism of integrable boundary only leads to a real reduction of the model:all the equations are reduced to real equations.

关 键 词：非线性薛定谔方程 可积方程族 可积边界条件 半直线问题 孤子解 

分 类 号：O29[理学—应用数学]