Multiwave, rogue wave, periodic wave, periodic cross-lump wave, periodic cross-kink wave, lump soliton, breather lump, homoclinic breather, periodic cross-kink, M-shaped rational solutions and their interactions for the Degasperis–Procesi equation

Abstract

We examine multiwave (MW), rogue wave (RW), periodic wave (PW), homoclinic breather (HB), breather lump wave (BLW), [Formula: see text]-shaped rational solutions, lump soliton, kink cross-rational (KCR), periodic cross-kink rational (PCKR), periodic cross-rational (PCR) solutions for the Degasperis–Procesi (DP) equation in shallow water waves through appropriate polynomial function scheme. We also compute some interactions for stated model including interaction of [Formula: see text]-shaped soliton with one kink, interactional solution with two kinks also lump soliton with kink one and kink two solutions. Furthermore, we made suitable 3D, 2D and contour profiles via appropriate parameters.