Bright and dark soliton solutions for variable-coefficient diffusion-reaction and modified Korteweg-de Vries equations

In this paper, by using a solitary wave ansatz in the form of sechp and tanhp functions, we obtain the exact bright and dark soliton solutions for the considered model, respectively. The topological (dark) and non-topological (bright) soliton solutions to the variable-coefficient diffusion-reaction equation and the variable-coefficient modified Korteweg-de Vries equation with power law nonlinearity are obtained by using the solitary wave ansatz method. The parametric conditions for the formation of soliton pulses are determined. Note that it is always useful and desirable to construct exact analytical solutions, especially soliton-type envelope ones, for understanding most nonlinear physical phenomena. (paper)