Lie-Bäcklund symmetries, analytical solutions and conservation laws to the more general (2 + 1)-dimensional Boussinesq equation

Abstract

The propagation of shallow water waves with small amplitudes as they propagate in a water channel of constant depth at a uniform speed is described by general Boussinesq equation. It also models the simulation of water waves in shallow seas and harbors for ocean engineering. In this work the symmetry analysis method is used to study the Lie-Bäcklund symmetry generators along with the corresponding conservation laws (cLs) for the governing equation by using a new conservation theorem. Moreover, by means of two effective analytical schemes namely the extended ShGEEM and the Kudryashov's methods, we construct some important soliton solutions for the equation. The physical features of the acquired solutions are plotted to depict the clear outlook of the solutions.