Variable-coefficient Polynomial Function Method for Finding the Lump-Type Solutions of Integrable System with Variable Coefficients

In this work, we study a ([Formula: see text])-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics. The new lump and lump-soliton solutions are obtained by the variable-coefficient polynomial function method. We used 3D graphs, contour plots and density graphs to show that the amplitude and velocity of solitons are affected by some variable coefficients. It is proved that the polynomial function method with variable coefficients is very direct and effective for solving lump-type solutions in variable coefficient integrable systems, and more new conclusions can be obtained.