LAUSR

Abstract The present article deals with M -lump solution and N -soliton solution of the (2+1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation by virtue of Hirota bilinear operator method. The obtained solutions for solving the current equation represent some localized waves including soliton, breather, lump and their interactions in which have been investigated by the approach of long wave limit. Mainly, by choosing specific parameter constraints in the M -lump and the N -soliton solutions, all cases the 1-breather or 1-lump can be captured from the 2-, 3-, 4- and 5-soliton. The obtained solutions are extended with numerical simulation to analyze graphically, which results into localized waves and their interaction from the 2-, 3-, 4- and 5-soliton solutions profiles. That will be extensively used to report many attractive physical phenomena in the fields of acoustics, heat transfer, fluid dynamics, classical mechanics and so on.