General M-lumps, T -breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation*

Abstract

A special transformation is introduced and thereby leads to the N-soliton solution of the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt (KDKK) equation. Then, by employing the long wave limit and imposing complex conjugate constraints to the related solitons, various localized interaction solutions are constructed, including the general M-lumps, T-breathers, and hybrid wave solutions. Dynamical behaviors of these solutions are investigated analytically and graphically. The solutions obtained are very helpful in studying the interaction phenomena of nonlinear localized waves. Therefore, we hope these results can provide some theoretical guidance to the experts in oceanography, atmospheric science, and weather forecasting.