Some symmetries, similarity solutions and various conservation laws of a type of dispersive water waves

Abstract

Abstract We investigate the point symmetries, Lie–Bäcklund symmetries for a type of dispersive water waves. We obtain some Lie transformation groups, various group-invariant solutions, and some similarity solutions. Besides, we produce different formats of conservation laws of the dispersive water waves by using different schemes. Finally, we consider some special solutions of the stationary dispersive water-wave equations.

Keywords

• Symmetry
• Similarity solution
• Conservation law