Interactions of rogue and solitary wave solutions to the (2 + 1)-D generalized Camassa–Holm–KP equation

Abstract

This research explores a (2+1)-d generalized Camassa-Holm-Kadomtsev-Petviashvili (gCHKP) model. We use a probable transformation to build bilinear formulation to the model by Hirota bilinear technique. We derive a single lump waves, multi-solitons solutions to the model from this bilinear form. We present various dynamical properties of the model such as one-, two-, three-, four-solitons. The double periodic breather waves, periodic line rogue wave, interaction between bell soliton and double periodic rogue waves, rogue and bell soliton, rogue and two bell solitons, two rogues, rogue and periodic wave, double periodic waves, two pair of rogue waves as well as interaction of double periodic rogue waves are established in a line. Among the results, most of the properties are unexplored in the prior research. Furthermore, with the assistance of Maple Software, we put out the trajectory of the obtained solutions for visualized the achieved dynamical properties.

Fusion and fission phenomena in a (2+1)-dimensional Sawada-Kotera type system

“…From equations (25)- (26), it is clear that setting A 3 to zero, while keeping the other coefficients nonzero, can lead to an inelastic interaction between a soliton and a dromion. Furthermore, it can be inferred that the two waves exchange both energy and velocity during the interaction process.…”

“…Recent research demonstrates that the derivation of lump solutions is achievable through the quadratic functions ansatz, as illustrated by the Kadomtsev-Petviashvili (KP) equation [23][24][25]. Subsequently, these findings have prompted a comprehensive exploration of lump excitations and interaction solutions between lumps and other types of nonlinear waves [26][27][28][29][30]. For example, Hossen obtained three types of interaction solutions to a (3+1)-dimensional model, including the lump-kink wave solution, breathers, and a new interaction solution among the lumps, kink waves and periodic waves [29].…”

Higher rogue and rogue-soliton interaction solutions of a (2 + 1) dimensional nonlinear model in fluid mechanics

“…It is a hot research topic about the interaction between rogue wave and other nonlinear waves. Such as, interaction solutions between rogue wave and soliton are obtained [16][17][18][19][20][21]. Interaction solutions between rogue wave and breather are discussed [22][23][24][25][26].…”

Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

“…To do that, the extended direct algebraic scheme [14], the novel extended Kudryashov's scheme [15], the expansion integral scheme [16], the Sine-Gordon expansion scheme [17], the Bäcklund transformations method [18], the bifurcation analysis scheme [19], the computational approach [20], and the unified approach [21] are applied. In general, several mathematical approaches have been developed in this context for deriving various nonlinear wave phenomena [22][23][24][25][26][27][28]. Due to the latest and most effective technique, the unified scheme is better for complex integral nonlinear dynamical models.…”