Soliton molecules and some novel hybrid solutions for the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation

Abstract

Soliton molecules have become one of the hot topics in recent years. In this article, we investigate soliton molecules and some novel hybrid solutions for the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt (gKDKK) equation by using the velocity resonance, module resonance, and long wave limits methods. By selecting some specific parameters, we can obtain soliton molecules and asymmetric soliton molecules of the gKDKK equation. And the interactions among N-soliton molecules are elastic. Furthermore, some novel hybrid solutions of the gKDKK equation can be obtained, which are composed of lumps, breathers, soliton molecules and asymmetric soliton molecules. Finally, the images of soliton molecules and some novel hybrid solutions are given, and their dynamic behavior is analyzed.

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

“…the solution of Θ-order y-type molecules and Γ-order breather molecules can be obtained. Under the expression of (18), when Θ = Γ = 1, the solution of the composition of one-order y-type molecule and one-order breather molecule is shown in Fig. (7).…”

“…With the help of these methods, hybrid solutions of various molecules have also been studied [18][19][20][21].…”

Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

“…Many scholars have studied (2+1)-dimensional gKDKK equation from different angles. Ma et al obtained soliton molecules and some novel hybrid solutions [33,34]. Liu et al analysed the lump, lumpoff and rogue waves with predictability [35].…”

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

“…The linear superposition principle can be used for constructing the resonance solutions [27][28][29]. The hybrid solutions consisting of soliton molecules and lump waves were investigated by partial velocity resonance and partial long wave limits [30,31]. It is interesting that Li et al considered a more generalized constraint of the parameters in N -solitons to construct the resonance Y -type soliton solutions and the hybrid solutions among the resonance Y -type solitons, breathers, soliton molecules and lumps [32,33].…”