Investigation of soliton structures for dispersion, dissipation, and reaction time-fractional KdV–burgers–Fisher equation with the noise effect

Abstract

ABSTRACT In this manuscript, the soliton structures for the time-fractional KdV–Burgers–Fisher equation with the effect of noise are investigated analytically. This is the dispersion–dissipation–reaction model. The third- and fifth-order time-fractional stochastic KdV–Burgers–Fisher equations are under consideration. These wave structures are constructed with the help of an extended generalized Riccati equation mapping method (EGREM). This method is a combined form of the G ′ / G expansion method with the generalized Riccati equation mapping method, and it will give the different forms of wave structures like shock, singular, combo, hyperbolic, trigonometric, mixed trigonometric, and rational solutions. These techniques are used symbolically with computational tools like Mathematica to demonstrate the efficiency and simplicity of the proposed strategy. Additionally, with the various relevant parameter values, the sketches of some solutions in the form of 3D and contour representations for the purpose of comprehending physical processes are drawn. These sketches clearly show the random behavior of these wave structures that are appearing in dispersion, dissipation, and reaction concentrations of these mathematical models.