Singular soliton, shock-wave, breather-stripe soliton, hybrid solutions and numerical simulations for a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system in fluid mechanics

Abstract

In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With the help of the Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on the finite difference method, we get some numerical one-soliton solutions. We graphically show the singular and shock-wave solutions, and observe that the singular one-soliton solutions are explosive and unstable, but the shock-wave solutions are non-singular and stable. We observe that the breather-stripe soliton moves along the negative direction of the y axis, where y is a variable, and the amplitude and shape of the breather-stripe soliton remain invariant during the propagation. We graphically demonstrate the interaction among a rogue wave, a periodic wave and a pair of the stripe solitons: the rogue wave arises from the one stripe soliton; the rogue wave interacts with the periodic wave, the rogue wave splits into two waves and then the two waves merge into a wave; the rogue wave fuses with the other stripe soliton. We graphically present the numerical one-soliton solutions which agree with the analytic one-soliton solutions.