Construction of Exact Solutions to Partial Differential Equations with CRE Method

Abstract

In this article, the consistent Riccati expansion (CRE) method is presented for constructing new exact solutions of (1+1) dimensional nonlinear dispersive modified Benjamin Bona Mahony (DMBBM) and mKdV-Burgers equations. The exact solutions obtained are composed of hyperbolic and exponential functions. The outcomes obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear partial differential equations.

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

“…Existing literature, exemplified by Khan et al [31], has discussed characteristics of trigonometric and hyperbolic type solutions with dark and bright solitons. Moreover, hyperbolic solutions have been reported by [32,33]. However, our findings stand out as we discovered dark, bright, and rogue wave solutions, setting them apart from earlier research.…”

“…The improved simple equation method was utilized by Khan et al [31] to identify accurate traveling wave solutions for the coupled Klein-Gordon equations and the NDMBBM equation. To create novel, accurate solutions to the NDMBBM problem and the mKdV-Burgers equation, Filiz and Arzu [32] used the consistent Riccati expansion approach. Kumar et al [33] used the sinh-Gordon function method to validate the stability analysis and discover numerical and fresh closed-form trigonometric function solutions of the NDMBBM equation.…”

Generalized Exp-Function Method to Find Closed Form Solutions of Nonlinear Dispersive Modified Benjamin–Bona–Mahony Equation Defined by Seismic Sea Waves

“…The modified simple equation (MSE) method was applied by Khan et al [23] to find exact travelling wave solutions of the nonlinear DMBBM equation and coupled Klein-Gordon equations. Filiz and Arzu [24] utilized the consistent Riccati expansion method for erecting new exact solutions of mKdV-Burgers equations and nonlinear DMBBM equation. The sinh-Gordon function method was used by Yokus et al [25] to check the stability analysis to find numerical and new closed form trigonometric function solutions of nonlinear DMBBM equation.…”