Collision and propagation of electromagnetic solitons in an antiferromagnetic spin ladder medium

Soliton collisions constitute one of the central topics of nonlinear-wave dynamics. We demonstrate an inelastic collision between the electromagnetic solitons in a two coupled Heisenberg spin ladder. The interplay of bilinear ferromagnetic coupling with antiferromagnetic rung and diagonal coupling along with the magnetic field component of the electromagnetic wave (EMW) has been studied by solving the Maxwell’s equation together with the two coupled Landau–Lifshitz nonlinear spin equations for the magnetization of the medium. The magnetization dynamics of the spin ladder under the influence of EMW is governed by a two coupled generalized derivative nonlinear Schro¨dinger (CGDNLS) equations. We employ the Ba¨cklund transformation to solve CGDNLS equations and construct the one and two-soliton solutions. We explicitly construct two soliton solutions to the CGDNLS equations in the framework of Hirota’s bilinearization method. We bring out clearly the various features underlying the fascinating shape changing collisions of electromagnetic solitons both in the absence and presence of antiferromagnetic diagonal coupling.