Solitons of the Modified KdV Equation with Variable Coefficients

Nonlinear waves are one of nature's most fundamental phenomena and their propagation in dynamical systems has sparked the researcher's interest. This article establishes the three soliton solutions (dark, bright, and singular) of MKdV equation with variable coefficient using the ansatz approach with inverse width, amplitude, and velocity and then establishing the graphs with the variation of inverse width, amplitude, and velocity. The solutions of the present study will become very helpful for various engineering applications and for the research community interested toward this field, especially in the field plasma of physics.