Complex Kraenkel-Manna-Merle system in a ferrite: N-fold Darboux transformation, generalized Darboux transformation and solitons

Abstract

Ferromagnetic materials such as the ferrites are used in the electronic and energy industries. Here, we concentrate on a complex Kraenkel-Manna-Merle system in a ferrite, under some coefficient constraints. An N-fold Darboux transformation of that system is presented via an existing Lax pair, where N is a positive integer. An N-fold generalized Darboux transformation, which admits one spectral parameter, is proposed through a limit procedure. One-, two- and three-soliton solutions of that system are determined via that N-fold Darboux transformation. The second-order and third-order degenerate soliton solutions of that system are derived via that N-fold generalized Darboux transformation. Those solitons are graphically represented for the magnetization and external magnetic field related to a ferrite.