Novel y-type and hybrid solutions for the $$(2+1)$$-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Abstract

In this paper, the research object is \((2+1)\)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation. After adding new constraint, new solutions which contain y-type molecules are obtained. The process of lump molecules and y-type molecules before and after the collision is studied by long-wave limit method, and the kinetic behavior analysis is given. The interactions between y-type molecules and resonant soliton molecules, y-type molecules and breather molecules are obtained by combining velocity resonance method and mode resonance method, respectively. Finally, a novel hybrid solution containing lump molecule, breather molecule and y-type molecule is given, and the kinetic behavior is shown.