In this paper, a (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada system is investigated in fluid mechanics via the symbolic computation. With help of Hirota method, we derive some singular soliton, shock-wave, breather-stripe soliton and hybrid solutions. Based on finite difference get numerical one-soliton We graphically show shock-wave solutions, observe that solutions are explosive unsta...