Inverse scattering transformation for generalized nonlinear Schrödinger equation

Xiaoen Zhang; Yong Chen

doi:10.1016/j.aml.2019.06.014

Inverse scattering transformation for generalized nonlinear Schrödinger equation

Xiaoen Zhang
, Yong Chen^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University
Zhejiang Normal University

Research output: Contribution to journal › Article › peer-review

112 Scopus citations

Abstract

Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only need the elementary Darboux transformation but not with the limit progress, which is more convenient than before. By choosing different parameters c₁ and c₂ appeared in the Darboux matrix, the 2n and 2n−1 order rogue waves are derived respectively. Furthermore, the general breather is also given with a different spectral parameters.

Original language	English
Pages (from-to)	306-313
Number of pages	8
Journal	Applied Mathematics Letters
Volume	98
DOIs	https://doi.org/10.1016/j.aml.2019.06.014
State	Published - Dec 2019

Keywords

Breather
Generalized Schrödinger equation
Nonzero-boundary condition
Robust inverse scattering transformation method
Rogue wave

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10.1016/j.aml.2019.06.014

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title = "Inverse scattering transformation for generalized nonlinear Schr{\"o}dinger equation",

abstract = "Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schr{\"o}dinger equation with nonzero boundary is given. Using this method, we only need the elementary Darboux transformation but not with the limit progress, which is more convenient than before. By choosing different parameters c1 and c2 appeared in the Darboux matrix, the 2n and 2n−1 order rogue waves are derived respectively. Furthermore, the general breather is also given with a different spectral parameters.",

keywords = "Breather, Generalized Schr{\"o}dinger equation, Nonzero-boundary condition, Robust inverse scattering transformation method, Rogue wave",

author = "Xiaoen Zhang and Yong Chen",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2019",

month = dec,

doi = "10.1016/j.aml.2019.06.014",

language = "英语",

volume = "98",

pages = "306--313",

journal = "Applied Mathematics Letters",

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T1 - Inverse scattering transformation for generalized nonlinear Schrödinger equation

AU - Zhang, Xiaoen

AU - Chen, Yong

PY - 2019/12

Y1 - 2019/12

N2 - Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only need the elementary Darboux transformation but not with the limit progress, which is more convenient than before. By choosing different parameters c1 and c2 appeared in the Darboux matrix, the 2n and 2n−1 order rogue waves are derived respectively. Furthermore, the general breather is also given with a different spectral parameters.

AB - Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrödinger equation with nonzero boundary is given. Using this method, we only need the elementary Darboux transformation but not with the limit progress, which is more convenient than before. By choosing different parameters c1 and c2 appeared in the Darboux matrix, the 2n and 2n−1 order rogue waves are derived respectively. Furthermore, the general breather is also given with a different spectral parameters.

KW - Breather

KW - Generalized Schrödinger equation

KW - Nonzero-boundary condition

KW - Robust inverse scattering transformation method

KW - Rogue wave

UR - https://www.scopus.com/pages/publications/85068234120

U2 - 10.1016/j.aml.2019.06.014

DO - 10.1016/j.aml.2019.06.014

M3 - 文章

AN - SCOPUS:85068234120

SN - 0893-9659

VL - 98

SP - 306

EP - 313

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Inverse scattering transformation for generalized nonlinear Schrödinger equation

Abstract

Keywords

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