Solitons for a generalized reaction–diffusion equation with the higher‐order power‐law nonlinearity in (1+1)‐ and (2+1)‐dimensional systems

Abstract

For the systems modeled by a generalized reaction–diffusion equation with the higher‐order quintic nonlinearity, we explore the soliton dynamics via the F‐expansion method. By the novel F‐base function ansatz, we first derived the bright soliton and kink soliton solutions for the one‐dimensional case of the reaction–diffusion equation with quintic nonlinearity. Furthermore, we employed self‐similar techniques to analyze the higher‐dimensional dynamics of bright soliton and kink soliton solutions supported by the (2+1)‐dimensional reaction–diffusion equation system with quintic nonlinearity. Additionally, we conducted stability analysis of derived soliton solutions. Our theoretical results demonstrate that under certain parametric setting, the reaction–diffusion equation model with higher‐order nonlinearity supports bright soliton and kink soliton in higher‐dimensional as well as lower dimensional setting, which provides guidance for observing and investigating soliton behavior in systems modeled by the reaction–diffusion equation with higher‐order quintic nonlinearity.