Interaction among a lump, periodic waves, and kink solutions to the KP-BBM equation

Abstract

The Hirota bilinear method is prepared for searching the diverse soliton solutions to the (2+1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation. Also, the Hirota bilinear method is used to find the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and one-kink soliton solutions are investigated. Also, the solitary wave, periodic wave, and cross-kink wave solutions are examined for the KP-BBM equation. The graphs for various parameters are plotted to contain a 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types of solutions, by solving the underdetermined nonlinear system of algebraic equations with the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions, and the interaction behaviors are revealed. The existing conditions are employed to discuss the available got solutions.

Diverse high-order soliton solutions and novel hybrid behaviors for the (2+1)-dimensional KP-BBM equation

“…Saut and Tzvetkov [25] used the globally well-posed frameworks of the conservation law to derive localized solitary solutions and produced soliton solutions according to the chosen arbitrary functions. Li et al studied its the lump and interaction with two stripe soliton solutions by the Hirota bilinear method [26]. Yu et al exp-function method [27] to probe into its generalized solitary solutions, periodic solutions and other exact solutions.…”

Dynamical interaction of solitary, periodic, rogue type wave solutions and multi-soliton solutions of the nonlinear models

“…Many scientific experimental models are employed in nonlinear differential equations (NLDEs) form including nonlinear fibers optics large-amplitude wave motions, fluids, plasma, solid-state physics etc. therefore, in the previous several times, many scientists and researchers worked to discover new effective methods [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] for explaining (NLDEs) which are significant to elucidate different intricate problem such as F-expansion method and exp-expansion method [1] , modified (g′/g)-expansion method [2] , improved differential transform method [3] , modified double sub-equation method [4] , extended (g′/g)-expansion method [5] , generalized (g′/g)-expansion method [6] , new generalized (g′/g)-expansion method [7] , discrete algebraic framework [8] , modified simple equation method [9] , hirota differential operator scheme [10] , IRM-CG method [11] , tanh method [12] , tanh and the sine–cosine methods [13] , hirota bilinear [14] , [15] , [16] , EMSE method [17] , generalized Riccati equation mapping method [18] , nonlinear capacity method [19] and so on.…”