Lie-Backlund symmetries, analytical solutions and conservation laws to the more general (2

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-Backlund 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.

Automated summary

In this work, the Lie-Backlund symmetry generators and corresponding conservation laws for the general Boussinesq equation are studied using a new conservation theorem and symmetry analysis method. Some important soliton solutions for the equation are constructed by means of two effective analytical schemes, and the physical features of these solutions are plotted to provide a clear outlook.