An investigation of the variable coefficients modified KdV equation arising in arterial mechanics by using two expansion techniques

Abstract

This article investigates the exact soliton solutions to the mKdV equation with time-dependent coefficients using the adapted sine-Gordon and modified simple equation approaches. The variations of the achieved solutions are demonstrated by plotting them with the corresponding solutions of the constant coefficients mKdV equation. Solitary waves with discrete wave profiles are developed from the resultant solution functions when specific values are assigned in place of the variable coefficients. The compatible two- and three-dimensional configurations show that the wave profiles are strongly affected by the variable wave velocity and its associated variable parameters. The analysis and interpretation emphasize the importance of the nonlinear evolution equations with time-varying coefficients, and it might open the purview to a notable domain of research.