Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized ‐expansion method

In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients modified Kawahara equation (VCMKE), which arise in modeling of various physical phenomena, are studied by Lie group analysis. The similarity reductions and exact solutions are derived by determining the complete sets of point symmetries of these equations. Moreover, some exact analytic solutions are considered by the power series method. Further, a generalized ‐expansion method is applied to VCKE and VCMKE for constructing some new exact solutions. As a result, hyperbolic function solutions, trigonometric function solutions and some rational function solutions with parameters are furnished. Copyright © 2012 John Wiley & Sons, Ltd.