New travelling wave solutions for fractional regularized long-wave equation and fractional coupled Nizhnik-Novikov-Veselov equation

Abstract

In this paper, solitary-wave ansatz and the (G ′ /G) −expansion methods have been used to obtain exact solutions of the fractional regularized long-wave (RLW) and coupled Nizhnik-Novikov-Veselov (NNV) equation. As a result, three types of exact analytical solutions such as rational function solutions, trigonometric function solutions, hyperbolic function solutions are formally derived from these equations. Proposed methods are more powerful and can be applied to other fractional differential equations arising in mathematical physics.

On new analytical solutions of fractional systems in shallow water dynamics

“…The main objective of this article is to introduce the implementation of the ERF method for obtaining new analytical wave solutions. We study the exact solutions of the nonlinear coupled time-fractional B-B equation [35], the nonlinear time-fractional ALW equation [36], and the nonlinear (2 + 1)-dimensional space-time fractional GNNV equation [37], which are frequently used in fluid dynamics and the propagation of SWWs [38,39]. There are many inspiring studies in the literature in which these proposed models are constructed with different definitions of fractional derivatives.…”

SITEM for the Conformable Space-Time fractional (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equations

“…Generalized exp-function method has been applied to the space-time fractional ANNV equations [18]. Solitary-wave ansatz method, the (G /G) expansion method and sub equation method have been used to obtain exact solutions of the space-time fractional GNNV equations [19,20]. Exp-function method, (G /G) expansion method and homotopy analysis method have been applied to the time fractional GNNV [21,22].…”