Analytic investigation of the (2+1)-dimensional Schwarzian Korteweg–de Vries equation for traveling wave solutions

Abstract

a b s t r a c tBy means of the two distinct methods, the Exp-function method and the extended (G 0 /G)-expansion method, we successfully performed an analytic study on the (2 + 1)-dimensional Schwarzian Korteweg-de Vries equation. We exhibited its further closed form traveling wave solutions which reduce to solitary and periodic waves. New rational solutions are also revealed.

New Double-Periodic Soliton Solutions for the (2+1)-Dimensional Breaking Soliton Equation

“…Many important and interesting properties for these obtained solutions are revealed with some figures (see Figs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] by the help of symbolic computation software Mathematica. The special ansätz functions method is simple and straightforward than the others method.…”

Diversity soliton excitations for the (2+1)-dimensional Schwarzian Korteweg-de Vries equation

“…The integrability of eq. (1) is proved by Toda and Yu [17] in the sense of Weiss-Tabor-Carnevale Painleve expansion, and the solution properties has been investigated [18][19][20][21].…”

Multi-Peak and Propagation Behavior of M-Shape Solitons in (2 + 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem

“…Many researchers worked on the ISKDV model. Ramirez et al investigated multiple solutions for the SKDV equation in (2 + 1)-dimensions [29] via Mobius transformation, Khater worked on new solitary solutions for a (2 + 1)-dimensional ISKDV-model via the Khater technique and Bernoulli sub-equation technique [30], Attia et al studied numerical and computational solutions for a (2 + 1)-dimensional ISKDV-model with Miura transform [31], Toda et al investigated the soliton solutions for a governing model in (2 + 1)-dimensions [32] via Lax pairs and well-known higher-dimensional manner, Gandarias et al founded the classical symmetry reductions for the ISKDV model by using symmetries and arbitrary functions [33], Li et al studied the soliton solutions of the (2 + 1)-dimensional ISKDV-model by applying Darboux transformation [34], Li et al evaluated the diversity soliton excitations for the (2 + 1)-dimensional ISKDV-model [35], and Aslan worked on an investigation of analytic solutions for the (2 + 1)-dimensional ISKDV-model via improved mapping approach [36], but the contribution of this document is to evaluate MS, HB, and M−shaped solitons by applying the symbolic computation with ansatz functions approach and logarithmic transformation for the (2 + 1)-dimensional ISKDV-model. M-shape rational solitons are described by nonlinear equations that involve both the phase and amplitude of the wave.…”