Breather wave, lump - periodic solutions and some other interaction phenomena to the Caudrey – Dodd – Gibbon equation

Abstract

Hirota’s bilinear method is used in this paper to obtain some breather wave and lumps solutions to the Caudrey–Dodd–Gibbon equation through the symbolic Mathematica 12 package. This equation is converted into its potential version and then the transformation of Cole–Hopf is implemented on the equation to produce its bilinear form. We then formally derive some novel solutions such as breather-wave, lump-periodic and some interaction solutions. The details explanation of the acquired solutions are also illustrated graphically in order to show the physical features of the solutions.