Resonance Y-shape solitons and mixed solutions for a (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada equation in fluid mechanics

Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey–Dodd–Gibbon–Kotera–Sawada(gCDGKS) equation in fluid mechanics is given. By defining a novel restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the new proposed constraint, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves and breather solutions are found. Finally, with the support of long-wave limit method, the interaction between resonant Y-type solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived. These new results greatly extend the exact solution of (2+1)-dimensional gCDGKS equation already available in the literature and provide new ideas for studying the dynamical behaviors of fluid mechanic, soliton and shallow water wave and so on.