Novel evolutionary behaviors of the mixed solutions to a generalized Burgers equation with variable coefficients

Abstract

A generalized Burgers equation with variable coefficients is introduced based on the (2+1)-dimensional Burgers equation. Using the test function method combined with the bilinear form, we obtain the lump solutions to the generalized Burgers equation with variable coefficients. The amplitude and velocity of the extremum point are derived to analyze the propagation of the lump wave. Moreover, we derive and study the mixed solutions including lump-one-kink and lump-two-kink cases. With symbolic computation, two cases of relations among the parameters are yielded corresponding to the solutions. Different and interesting interaction phenomena arise from assigning abundant functions to the variable coefficients. Especially, we find that the shape of kink waves might be parabolic type, and one lump wave can be decomposed into two lump waves. The test function method is applicable for the generalized Burgers equation with variable coefficients, and it will be applied to some other variable-coefficient equations in the future.