Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 2, January 2020, Pages 279 - 294

A generalization of the Landau-Lifschitz equation: breathers and rogue waves

Authors
Ruomeng Li, Xianguo Geng*, Bo Xue
School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, Henan 450001, People’s Republic of China,liruomeng@zzu.edu.cn(RM Li);xggeng@zzu.edu.cn(XG Geng);xuebo@zzu.edu.cn(B Xue)
*Corresponding author (xggeng@zzu.edu.cn)
Corresponding Author
Xianguo Geng
Received 9 June 2019, Accepted 11 September 2019, Available Online 27 January 2020.
DOI
10.1080/14029251.2020.1700636How to use a DOI?
Keywords
generalized uniaxial Landau-Lifschitz equation; N-fold generalized Darboux transformation; Akhmediev breathers; solitons; rogue waves
Abstract

A generalization of the Landau-Lifschitz equation with uniaxial anisotropy is proposed, which can also reduce to the derivative nonlinear Schrödinger equation under an infinitesimal parameter. Based on the gauge transformation between Lax pairs, an N-fold generalized Darboux transformation is constructed for the generalization of the Landau-Lifschitz equation with uniaxial anisotropy. As applications of the N-fold generalized Darboux transformations, several types of exact solutions of the generalization of the Landau-Lifschitz equation with uniaxial anisotropy are obtained, including soliton solutions, Akhmediev breather solutions and rogue-wave solutions.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 2
Pages
279 - 294
Publication Date
2020/01/27
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1700636How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Ruomeng Li
AU  - Xianguo Geng
AU  - Bo Xue
PY  - 2020
DA  - 2020/01/27
TI  - A generalization of the Landau-Lifschitz equation: breathers and rogue waves
JO  - Journal of Nonlinear Mathematical Physics
SP  - 279
EP  - 294
VL  - 27
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1700636
DO  - 10.1080/14029251.2020.1700636
ID  - Li2020
ER  -