Construction of breather solutions and N-soliton for the higher order dimensional Caudrey-Dodd-Gibbon-Sawada-Kotera equation arising from wave patterns

Abstract

In this research, we explore the dynamics of Caudrey-Dodd-Gibbon-Sawada-Kotera equations in (1 + 1)-dimension, such as N-soliton, and breather solutions. First, a logarithmic variable transform based on the Hirota bilinear method is defined, and then one, two, three and N-soliton solutions are constructed. A breather solution to the equation is also retrieved via N-soliton solutions. All the solutions that have been obtained are novel and plugged into the equation to guarantee their existence. 2-D, 3-D, contour plot and density plot are also presented.