The Korteweg-de Vries–Caudrey–Dodd–Gibbon dynamical model: Its conservation laws, solitons, and complexiton

Abstract

The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions.