Painlevé Analysis, Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin—Bona—Mahony—Burger (BBMB) Equation

In this paper, a variable-coefficient Benjamin—Bona—Mahony—Burger (BBMB) equation arising as a mathematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated. The integrability of such an equation is studied with Painlevé analysis. The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method. Furthermore different types of solitary, periodic and kink waves can be seen with the change of variable coefficients.

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