A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS

PHYSICA D-NONLINEAR PHENOMENA

卷:320

Article

Soffer, Avy^1,2  Zhao, Xiaofei³ 

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[3] Univ Rennes 1, IRMAR, F-35042 Rennes, France

关键词: Moving soliton;    Radiation;    Multichannel dynamics;    Nonlinear Schrodinger equation;    Modulation equations;    Numerical method;   

DOI  :  10.1016/j.physd.2016.02.005

来源: Elsevier

【 摘 要 】

Based on our previous work for solving the nonlinear Schrodinger equation with multichannel dynamics that is given by a localized standing wave and radiation, in this work we deal with the multichannel solution which consists of a moving soliton and radiation. We apply the modulation theory to give a system of ODEs coupled to the radiation term for describing the solution, which is valid for all times. The modulation equations are solved accurately by the proposed numerical method. The soliton and radiation are captured separately in the computation, and they are solved on the translated domain that is moving with them. Thus for a fixed finite physical domain in the lab frame, the multichannel solution can pass through the boundary naturally, which cannot be done by imposing any existing boundary conditions. We comment on the differences of this method from the collective coordinates. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free