On Soliton Dynamics of the Generalized Fisher Equation with Time-dependent Coefficients

A generalized Fisher equation involving a nonlinear term of any order and timedependent coefficients is investigated. We present exact analytical solutions describing periodic and solitary wave solutions using the modified sine-cosine method. A certain class of exact soliton-like solutions has been found by means of the auxiliary equation method. The conditions of existence and uniqueness of these solutions are given. We exploit the temporal variation of the coefficients to study the dynamics of solitary waves in presence of the linear dispersion effect and arbitrary power nonlinearity. We show numerically that the time-variation of the dependent coefficients provides a physical way to control the solitary wave profile. These solitary waves are expected to find practical application in inhomogeneous nonlinear systems that are described by Fishertype equation.