Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain

Abstract

Spin waves, usually used in radar and communication system, are the collective excitation of spin system in ferromagnetic metals, and considered as potential data carriers for computing devices because they have nanometre wavelengths. In this paper, in a Heisenberg ferromagnetic spin chain, we study a matrix Lakshmanan-Porsezian-Daniel equation. With regard to the slowly-varying envelope of the wave, we work out the N-fold Darboux transformation, and then we construct the N-fold generalized Darboux transformation, where N is a positive integer. Furthmore, the first-, second- and third-order vector breathers are derived according to the generalized Darboux transformation method. We show the propagation for three kinds of the first- and second-order vector breathers, and also analyze the influence of the strength of the higher-order linear and nonlinear effects on the first- and second-order vector breathers. All our results rely on the strength of the higher-order linear and nonlinear effects in that equation. Our results may provide some help for people to study the nonlinear characteristics of magnetic materials.