TY - JOUR
T1 - A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS
AU - Soffer, Avy
AU - Zhao, Xiaofei
N1 - Funding Information:
A. Soffer is partially supported by NSF grant DMS 1201394 . X. Zhao is supported by the French ANR project MOONRISE ANR-14-CE23-0007-01 . The authors would like to thank the referees for their constructive comments and suggestions that greatly improved the paper. Part of this work was done when the authors were visiting the School of Mathematics and Statistics, Central China Normal University, China, 2015.
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/4/15
Y1 - 2016/4/15
N2 - Based on our previous work for solving the nonlinear Schrödinger 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.
AB - Based on our previous work for solving the nonlinear Schrödinger 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.
KW - Modulation equations
KW - Moving soliton
KW - Multichannel dynamics
KW - Nonlinear Schrödinger equation
KW - Numerical method
KW - Radiation
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U2 - 10.1016/j.physd.2016.02.005
DO - 10.1016/j.physd.2016.02.005
M3 - Article
AN - SCOPUS:84959450203
VL - 320
SP - 77
EP - 88
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
ER -