A generalized ([formula omitted])-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation: Multiple exp-function algorithm; conservation laws; similarity solutions

Abstract

A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–Petviashvili equation is ambassador of the higher dimensional Kadomtsev–Petviashvili hierarchy. This equation was acquired by a diminution for the well-known three-dimensional Kadomtsev–Petviashvili equation which illustrates the dissemination of nonlinear waves in plasmas and fluid dynamics. We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method. Finally, we compute conserved currents courtesy using the invariance and multiplier technique. The findings can well mimic complex waves and their dealing dynamics in fluids.