On the invariant analysis, symmetry reduction with group-invariant solution and the conservation laws for (2 + 1)-dimensional modified Heisenberg ferromagnetic system

Abstract

In this paper, a [Formula: see text]-dimensional modified Heisenberg ferromagnetic system, which appears in the biological pattern formation and in the motion of magnetization vector of the isotropic ferromagnet, is being investigated with the aim of exploring its similarity solutions. With the aid of Lie symmetry analysis, this system of partial differential equations has been reduced to a new system of ordinary differential equations, which brings an analytical solution of the main system. Infinitesimal generators, commutator table, and the group-invariant solutions have been carried out by using Lie symmetry approach. Moreover, conservation laws of the above mentioned system have been obtained by utilizing the new conservation theorem proposed by Ibragimov. By applying this analysis, the obtained results might be helpful to understand the physical structure of this model and show the authenticity and effectiveness of the proposed method.