Exact Soliton Solutions for a Spin Chain with an Easy Plane

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

“…Here using the similar method in Ref. [13,14] we obtain both the one-and two-soliton solutions (for detail see the appendix) denoted by S(n) with n = 1, 2 of Eq. (5) in the following form:…”

“…By introducing a particular parameter Huang [14] showed that the Jost solutions can be generated and the Lax equations are satisfied, and moreover constructed Darboux transformation matrices. An explicit expression of the one-soliton solution in terms of elementary functions of z and t was reported.…”

“…Before collision, they move towards each other, one with velocity V 1 and shape variation frequency Ω 1 and the other with V 2 and Ω 2 . In order to understand the nature of two-soliton interaction, we analyze the asymptotic behavior of two-soliton solution (14). Asymptotically, the two-soliton waves (14) can be written as a combination of two one-soliton waves (8) with different amplitudes and phases.…”

“…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.…”

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

“…It is demonstrated that the inverse scattering transformation [14,[19][20][21] can be used to solve the Landau-Lifschitz equation for an anisotropic spin chain. Great efforts [22,23] have been devoted to construct the soliton solution which are found by means of the Darboux transformation [24]. The continuum spin chain in an external magnetic field is of great interest and multi-soliton solutions of Landau-Lifschitz equation for an isotropic spin chain have been reported [25].…”