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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.

international journal of nonlinear sciences and numerical simulation

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