A generalization of the Landau-Lifschitz equation: breathers and rogue waves. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Li, Ruomeng; Geng, Xianguo; Xue, Bo
• Is Part Of: Journal of nonlinear mathematical physics. Volume 27:Issue 2(2020)
• Page Start: 279
• Page End: 294
• Publication Date: 2020-04-02
• Subjects: generalized uniaxial Landau-Lifschitz equation -- N-fold generalized Darboux transformation -- Akhmediev breathers -- solitons -- rogue waves; 37K35 -- 35Q51 -- 35Q58; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2020.1700636
• Languages: English
• ISSNs: 1402-9251

Abstract

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.