Analytical Treatment of the Generalized Hirota-Satsuma-Ito Equation Arising in Shallow Water Wave

Abstract

In the current study, an analytical treatment is studied starting from the 2 + 1 -dimensional generalized Hirota-Satsuma-Ito (HSI) equation. Based on the equation, we first establish the evolution equation and obtain rational function solutions by means of the bilinear form with the help of the Hirota bilinear operator. Then, by the suggested method, the periodic, cross-kink wave solutions are also obtained. Also, the semi-inverse variational principle (SIVP) will be utilized for the generalized HSI equation. Two major cases were investigated from two different techniques. Moreover, the improved tan χ ξ method on the generalized Hirota-Satsuma-Ito equation is probed. The 3D, density, and contour graphs illustrating some instances of got solutions have been demonstrated from a selection of some suitable parameters. The existing conditions are handled to discuss the available got solutions. The current work is extensively utilized to report plenty of attractive physical phenomena in the areas of shallow water waves and so on.

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.…”