(2+1)维非线性薛定谔方程的怪波解  

Strange Wave Solution for the (2+1)-dimensional Nonlinear Schrdinger Equation

作　　者：程丽[1] 张翼[2] 

机构地区：[1]金华职业技术学院师范学院,浙江金华321017 [2]浙江师范大学数理信息学院,浙江金华321004

出　　处：《长江大学学报（自科版）（上旬）》2016年第3期35-39,4,共5页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：国家自然科学基金项目(11371326)

摘　　要：应用Hirota双线性算子方法得到(2+1)维非线性薛定谔方程的周期解和其极限解,利用sato算子理论把(1+1)维非线性薛定谔方程的Grammian解转化为(2+1)维非线性薛定谔方程非奇异的有理解,从而得到(2+1)维非线性薛定谔方程的一阶和高阶怪波解。研究结果说明了高维的非线性薛定谔方程具有有理分式的怪波解,这些方法同样适用于其他的高维薛定谔型方程,如Mel’nikov方程、Fokas系统等。A class of cyclic and ultimate limit solutions in the(2+1)-dimensional nonlinear Schrdinger equation is derived by the Hirota bilinear method.The Sato Operator Theory is used to transform the Grammian solution in Grammian Nonlinear Schrdinger Equation into the non-stramge reasonable solution in(2+1)-dimensional nonlinear Schrdinger equation,therefore general high-order strange waves in the(2+1)-dimensional nonlinear Schrdinger equation are obtained.These methods are also suitable for other high-order Schrdinger Equations,such as Mel,Nikov Equations and Fokas System.

关 键 词：(2+1)维非线性薛定谔方程 HIROTA双线性方法 周期解 怪波解 

分 类 号：O175.24[理学—数学]