On the breather waves, rogue waves and solitary waves to a generalized (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Abstract

In this paper, we consider the generalized (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada(CDGKS) equation. By using the Bell polynomial, we derive its bilinear form. Based on the homoclinic breather limit method, we construct the homoclinic breather wave and the rational rogue wave solutions of the equation. Then by using its bilinear form, some solitary wave solutions of the CDGKS equation are provided by a very natural way. Moreover, some prominent characteristics for the dynamic behaviors of these solitons are analyzed by several graphics. Our results show that the breather wave can be transformed into rogue wave under the extreme behavior.