Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field

Abstract

We investigate dynamics of exact N-soliton trains in spin chain driven by a time-dependent magnetic field by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape-variation induced by the time varying field as well. In terms of the general soliton solutions N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears generally due to the time varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead a potential technique of shape control of soliton.

Exact soliton solution of spin chain with an external magnetic field in linear wave background

“…One of the integrable models for spin chain is Landau-Lifshitz equation [9] which has been studied by a variety of techniques such as inverse scattering transformation [3,10,11], Darboux transformation [12], Riemann-Hilbert approach [13], etc. Exact soliton solutions are reported for the isotropic [10,[14][15][16][17] and anisotropic [11][12][13]18,19] spin chains as well. The other integrable model is a type of NonlinearSchr} odinger equation studied in [3].…”

Magnetic soliton and soliton collisions of spinor Bose-Einstein condensates in an optical lattice

“…In particular, it explains the existence of ferromagnetism and antiferromagnetism at temperatures below the Curie temperature. The magnetic soliton [10], which describes localized magnetization, is an important excitation in the Heisenberg spin chain [11,12,13,14]. The Haldane gap [15] of antiferromagnets has been reported in integer Heisenberg spin chain.…”

Soliton dynamics and elastic collisions in a spin chain with an external time-dependent magnetic field

“…In a ferromagnetic spin chain, under the influence of a time-oscillating magnetic field with an arbitrary direction, the Heisenberg Hamiltonian takes the form [19] …”

“…(1) have been studied extensively in much literature and many monographs [5][6][7][8][9]. The relevant nonlinear waves are of current interest for magnetic systems under the action of an external magnetic field [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Regarding the motion of a continuum Heisenberg spin chain, people have paid attention towards the new effects of an external magnetic field on the nonlinear wave.…”