Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation
Xi-Hu Wu,
Yi-Tian Gao,
Xin Yu,
Cui-Cui Ding and
Liu-Qing Li
Chaos, Solitons & Fractals, 2022, vol. 162, issue C
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 Nth-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.
Keywords: Heisenberg spin chain; Lakshmanan-Porsezian-Daniel equation; Modified generalized Darboux transformation; Bound-state soliton; Degenerate soliton (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006099
DOI: 10.1016/j.chaos.2022.112399
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