Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.