Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation

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 interac-tion, 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 mul-tiple 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. In-fluence of beta on the type-I degenerate solitons are graphically illustrated, where beta denotes the strength of the higher-order linear and nonlinear effects in the equation.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, a Lakshmanan-Porsezian-Daniel equation describing the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain is investigated. The semirational solutions of the equation are discussed, including degenerate soliton solutions, interaction solutions among solitons and degenerate solitons, and bound state solutions among a set of degenerate solitons.