Darboux transformations and exact soliton solutions of integrable coupled spin systems related with the Manakov system

Abstract

We construct a Darboux transformation of a general $su(3)$-valued spin system called the $\Gamma$-spin system. Using this Darboux transformation we derive a recursive formula for the soliton solutions of this spin system. Then using these results we present explicit expressions for the 1-soliton solution of the coupled $su(2)$-valued spin systems, namely, of the coupled M-LIII equation.

9 pages

References in corpus (2)

• Integrable Motion of Curves in Self-Consistent Potentials : Relation to Spin Systems and Soliton Equations
• The Manakov system as two moving interacting curves

Cited by in corpus (3)

• Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions
• Zakharov-Ito equation and Generalized Heisenberg ferromagnet-type equation: equivalence and related geometric curve flows
• Generalized Heisenberg Ferromagnet type Equation and Modified Camassa-Holm Equation: Geometric Formulation, Soliton Solutions and Equivalence