Understanding general rogue wave solutions of the Gardner equation

Abstract

The Gardner equation is used as a generic model for internal waves and other phenomena. We find interesting structures revealed by rational solutions of this equation. We show the benefit of using the Hirota method to give simple forms, which are then used to generate the solutions. These forms are of lower order than the polynomials in the solutions themselves. Patterns and powers of these polynomials are discussed. A brief study of the poles of each solution elucidates the structure of various rogue wave solutions and allows us to gain understanding and insight regarding the fea-tures of such rogue waves. These solutions provided here have numerous applications in internal ocean waves and dusty-type plasmas. Show more