| Abstract: | We consider the Heisenberg ferromagnetic spin chain equation, which is governed by the (2+1)-dimensional nonlinear Schrödinger-type equation. Based on the Ablowitz–Kaup–Newell–Segur frame, we study the integrability of the equation by deriving its Lax pair and infinite conservation laws. By introducing a potential transformation, we obtain its Hirota bilinear form and soliton solutions. Based on the resulting lax pair, we construct Darboux transformation and multi-soliton solutions of the equation. Furthermore, we also find the other type of soliton solutions for the equation by considering its Bäcklund transformation. Finally, we discuss the linear stability analysis by considering its stability condition for the stationary solution of the equation, which can be used to analyze modulation instability. The technique presented in this work is analytical, which can be used to enrich the dynamical of the Heisenberg ferromagnetic spin chain equation. |
