Exact Solutions of the Nonlinear Modified Benjamin-Bona-Mahony Equation by an Analytical Method

Abstract

The current manuscript investigates the exact solutions of the modified Benjamin-Bona-Mahony (BBM) equation. Due to its efficiency and simplicity, the modified auxiliary equation method is adopted to solve the problem under consideration. As a result, a variety of the exact wave solutions of the modified BBM equation are obtained. Furthermore, the findings of the current study remain strong since Jacobi function solutions generate hyperbolic function solutions and trigonometric function solutions, as liming cases of interest. Some of the obtained solutions are illustrated graphically using appropriate values for the parameters.

Revisiting (2+1)-dimensional Burgers’ dynamical equations: analytical approach and Reynolds number examination

“…Analytically wise, a number of appealing approaches analytical exist in the open literature for solving diverse evolution equations and nonlinear Schr ö dinger equations. More so, let us recall some of the following wellknown approaches, including, the generalized Riccati equation approach [7][8][9], the modified tanh expansion approach [10][11][12], some integral-based methods approaches [11][12][13][14], the trial equation approach [15,16], the rational ( ) G G ¢ -expansion method [17,18], the Kudryashov analytical approach [19][20][21], the Lie's symmetry approach [22,23], the F-expansion approach [24], the Jacobi elliptic function technique, that is alternatively called the modified auxiliary equation technique [25][26][27][28], the extended exponential rational approach [29], the semi-inverse variational technique [30][31][32], and the first integral and functional variable approaches [33] to state a few; one would equally read [34][35][36][37] and the references therewith for more analytical approaches in this regard. On the other hand, a number of computational approaches are also visible for solving different evolution equations.…”