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

Author

Listed:
  • Wu, Xi-Hu
  • Gao, Yi-Tian
  • Yu, Xin
  • Ding, Cui-Cui
  • Li, Liu-Qing

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.

Suggested Citation

  • Wu, Xi-Hu & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Li, Liu-Qing, 2022. "Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006099
    DOI: 10.1016/j.chaos.2022.112399
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