(2+1)维非线性Schrödinger型方程的同宿轨道

doi:10.1007/s10483-008-1013-y

Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (10): 1383-1389 .doi: https://doi.org/10.1007/s10483-008-1013-y

• Articles • 上一篇

(2+1)维非线性Schrödinger型方程的同宿轨道

沈守枫;张隽

浙江工业大学应用数学系杭州 310023

收稿日期:2008-05-07 修回日期:2008-08-02 出版日期:2008-10-01 发布日期:2008-10-01
通讯作者: 沈守枫

Homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations

SHEN Shou-feng; ZHANG Jun

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, P. R. China

Received:2008-05-07 Revised:2008-08-02 Online:2008-10-01 Published:2008-10-01
Contact: SHEN Shou-feng

摘要/Abstract

摘要： 本文研究了几类(2+1)维非线性Schrödinger型方程同宿轨道的问题。利用Hirota双线性算子方法，通过给出的相关变换，得到了包括(2+1)维的长短波相互作用方程，广义Zakharov方程，Mel'nikov方程和g-Schrödinger方程的同宿轨道解的显式解析表达式，从而讨论了这些方程的同宿轨道.

关键词: 非线性Schrö, dinger型方程, 同宿轨道, Hirota双线性方法

Abstract: Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations are constructed based on Hirota's bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel'nikov equation, and g-Schrödinger equation are constructed based on Hirota's bilinear method.

Key words: Homoclinic orbit, Schrö, dinger-like equation, bilinear method

中图分类号:

O175
35Q53

沈守枫;张隽. (2+1)维非线性Schrödinger型方程的同宿轨道[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1383-1389 .

SHEN Shou-feng;ZHANG Jun. Homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(10): 1383-1389 .

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(2+1)维非线性Schrödinger型方程的同宿轨道

Homoclinic orbits for some (2+1)-dimensional nonlinear Schrödinger-like equations

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