M-breather, M-lump, breather molecules and their interaction solutions for a (2+1)-dimensional KdV equation

Abstract

Date-Jimbo-Kashiwara-Miwa (DJKM) equation is an integrable (2+1)- dimensional extension of the KdV equation and describes two-dimensional nonlinear dispersive waves. In this paper, we first derive the M-breather solution in terms of determinants for the DJKM equation applying the nonlinear superposition formula and analyze the dynamical properties of the breathers. The M-lump waves for the DJKM equation are obtained through the full degeneration of the breathers and hybrid solutions composed of line solitons, breathers and lumps are constructed. By using the velocity resonance mechanism, we also show that the DJKM equation possesses some resonant structures for breathers and solitons such as breather molecules and breather-soliton molecules. Furthermore, based on the N-soliton solution, the interactions between breather/breather-soliton molecules and breathers/lumps are investigated.

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

“…So far, the interactions between lump molecules and other molecules have also been studied in Ref. [42][43][44]. In this section, the interaction between lump molecules and novel y-type molecules will be explored, the process…”