Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation

Abstract

We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the $(G\mathrm{\text{'}}/G)$-expansion method.