Novel Soliton Solutions and Wave Interactions for the Nonlinear Fisher Equation Using Hirota’s Method: Applications in Plasma, Optics, and Material Sciences

Abstract

The nonlinear Fisher equation, which can be applied to crystallization, fluid dynamics, fiber optics, plasma, and biological population models, is of particular importance. We build bilinear equations using Hirota’s derivatives, and then we compute several kinds of solitons. We use the Hirota Bilinear Method (HBM) and the ansatz approach to develop Lump Solution (LS), Multi-Waves (MWs), Ma-Breathers (MBs), Kuznetsov-Ma-Breathers (KMBs), and Rogue Waves solutions (RWs) for the proposed model. In the domains of science and engineering, the developed wave solutions are highly significant. We also investigated the stability analysis of the proposed model by using the linear stability approach. Solutions for breathers could be applied to increase the effectiveness of solitons in plasma waves and optical communication systems. Lump wave solutions can be used to manipulate and control laser beams for material manufacturing or laser surgery, whereas rogue wave solutions can help ensure the safety of ships and oil rigs. Under certain constraints, we additionally investigate one, two, and other soliton interactions for suggested model. To anticipate the wave dynamics, specific 2D, 3D, and contour portraits are also examined with the help of computing software Mathematica. To regulate fusion as a potential energy source in the future, these interactions may be applied to plasma stability and containment. This work presents a novel contribution to the field by exploring soliton solutions of the nonlinear Fisher equation. To the best of our knowledge, this research has not been previously addressed in the literature. The suggested method provides a more powerful computational framework for examining Non Linear Evolution Equations (NLEEs) in engineering and mathematical sciences and yields a wide variety of solutions.