New topological and non-topological unidirectional-wave solutions for the modified-mixed KdV equation and bidirectional-waves solutions for the Benjamin Ono equation using recent techniques

Abstract

In this paper, new explicit unidirectional wave solutions for the modified-mixed KdV equation and bidirectional waves for the Benjamin Ono equation are studied. New extension of the rational sine-cosine and sinh-cosh methods are used. In addition, an extension of the recent polynomial function method is applied as well. Different types of topological and non-topological soliton solutions are extracted to the proposed models and categorized by providing 2D and 3D graphs. Finally, some physical properties of the new bidirectional waves solutions to the Benjamin Ono model are discussed.