Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation. (September 2022)

• Record Type: Journal Article
• Authors: Wu, Xi-Hu; Gao, Yi-Tian; Yu, Xin; Ding, Cui-Cui; Li, Liu-Qing
• Is Part Of: Chaos, solitons and fractals. Volume 162(2022)
• Publication Date: 2022-09
• Subjects: Heisenberg spin chain -- Lakshmanan-Porsezian-Daniel equation -- Modified generalized Darboux transformation -- Bound-state soliton -- Degenerate soliton; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112399
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, a Lakshmanan-Porsezian-Daniel equation, which describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction, is investigated. With respect to the coherent amplitude of the spin deviation operator for the ferromagnetic spin chain in the coherent state, we construct a modified generalized Darboux transformation in which the multiple spectral parameters are involved, and the N th-order semirational solutions in the determinant form, where N is a positive integer. Then, we obtain and analyze three types of the semirational solutions: Type-I degenerate soliton solutions which describe the degenerate solitons; Type-II degenerate soliton solutions which describe the interaction among the solitons and degenerate solitons; Type-III degenerate soliton solutions which describe the bound states among a set of the degenerate solitons. Generation conditions of the above semirational solutions are discussed. When the multiple solitons have the equal velocity, bound-state solitons are also constructed. Influence of β on the type-I degenerate solitons are graphically illustrated, where β denotes the strength of the higher-order linear and nonlinear effects in the equation.