Analytic Study on an Extended Higher-Order Nonlinear Schrödinger Equation for Heisenberg Ferromagnet

Abstract

Under investigation in this paper is an extended higher-order nonlinear Schrodinger equation, which describes the spin dynamics of a weak anisotropic Heisenberg ferromagnetic spin chain with site-dependent bilinear, biquadratic, and octupole-dipole interactions. Based on the Lax pair, infinitely many conservation laws are obtained. With the aid of an auxiliary function, bilinear forms and N-soliton solutions are presented explicitly. Figures are plotted to describe the bound states of the two and three solitons. Interaction periods and soliton separation factors of the bound states of solitons are analyzed. The third- and fourth-order perturbation coefficients α and γ are directly proportional to the soliton velocities; they influence the interaction periods, but do not affect the soliton amplitudes. Bound states of the solitons propagate with certain velocities, and the varying interaction periods are discussed. Finally, the condition for the modulation instability is given. These results may be useful for the spin dynamics in Heisenberg ferromagnets.