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Solitons and complexitons solutions of an integrable model of \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain. (English) Zbl 1398.37068

Summary: In this paper, we consider an integrable model of \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain. Using the ansatz method, bright and dark 1-soliton solutions are derived. Also, some conditions are given which guarantee the existence of solitons. In addition, some exact solutions also derived based on the sub-ODE method. At last, the explicit power series solutions also presented.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35C08 Soliton solutions
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C23 Exactly solvable dynamic models in time-dependent statistical mechanics
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