A generalization of the Landau-Lifschitz equation: breathers and rogue waves. Issue 2 (2nd April 2020) - Li, Ruomeng; Geng, Xianguo; Xue, Bo
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.