Resonant multi-soliton solutions to the (2 + 1)-dimensional Sawada–Kotera equations via the simplified form of the linear superposition principle

Abstract

In this work, a simplified form of the linear superposition principle is proposed to facilitate the computational work and make the resonant multi-soliton solutions easily generated. The (2+1)-dimensional Sawada-Kotera (SK) equation, one of fifth-order KdV-like equations describing the nonlinear wave phenomena in shallow water, ion-acoustic waves in plasmas, etc., is investigated. Moreover, in order to demonstrate the power of the proposed method, a new version of the SK equation is further considered and examined. The general forms of resonant multi-soliton solutions are formally established. Furthermore, by taking about reverse engineering of the generated solutions, various versions of the (2+1)-dimensional SK equation can be derived that may make great contributions to real physical phenomena and enrich the related nonlinear sciences. Finally, the propagations of two-and three-soliton waves are presented.

Abundant wave solutions to two novel KP-like equations using an effective integration method

“…Taking equation (86) and substituting the values of the parameters into equations (50) and (10), one obtains the following kink wave Dynamic behavior of the solution u 12 (x, y, z, t)for some specific parameter is shown in figure 12. So far, abundant new kink and periodic wave solutions are formally generated to the examined equations (5) and (8). It has to be emphasized that the forms of the investigated equations are similar but give different solutions, u 1−10 and u 1−12 , respectively.…”

Evolutionary behavior of rational wave solutions to the (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

“…Multiple wave solution: According to the linear superposition method [1][2][3][4][5][6][7][8][9], a polynomial corresponding to the Hirota bilinear equation ( 4) is considered as…”

“…Although there are different strategies to deal with nonlinear differential models, a specific strategy is deriving the Hirota bilinear form and then applying the linear superposition principle along with symbolic computations to acquire rational wave solutions. Recently, the LSM has been used by many authors and has the theme of many research works [1][2][3][4][5][6][7][8][9]. For example, a group of rational wave solutions to the Hirota-Satsuma-Ito equation and the asymmetric Nizhnik-Novikov-Veselov equation were obtained respectively in [8,9] by adopting the LSM along with symbolic computations.…”

Unexpected configurations for the optical solitons propagation in lossy fiber system with dispersion terms effect

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