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 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.

The excitation of high-order localized waves in (3+1)-dimensional Kudryashov-Sinelshchikov equation

“…Taking full account of Nsoliton, it is notable that no matter what real values the parameters of f N take, there is no appearance of breather waves. Fortunately, an effective idea called complexification method was proposed in [40] and has been successfully applied in many nonlinear systems [41][42][43]. It can be understood that the paired conjugation of parameters k i , r i , s i will generate glossy breather waves of Kudryashov-Sinelshchikov equation on a certain background.…”