Exact Traveling Wave Solutions to Benney- Luke Equation

Abstract

By using the improved (G/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.

Exact solutions of the Benney–Luke equation via (1/G')-expansion method

“…The BL equation appears in a variety study, such as exact solutions of BL equation were found by using enhanced   GG  -expansion method [26] analytic solutions of BL equation were obtained with the help of improved   GG  -expansion method [27], the exact solution was obtained using homogeneous balance method for BL equation [28], the shock wave solution of the BL equation was obtained using ansatz method [29], exact solutions of the BL equation were found by using modified simple equation method [24].…”

Modified Integral Transform for Solving Benney-Luke and Singular Pseudo-Hyperbolic Equations

“…"So far as the exact solutions to NLEEs are concerned, the data furnished in the present study pertaining to their structure will assist in preventing the structure from claiming changes attributable to unpredictable physical phenomena." Among these endeavours are the strategy of homotopy examining, the strategy of sticking, the variable strategy of reiteration [8][9][10][11][12], the differential transforms method and Laplace transform [13][14][15] differential transforms method, Elzaki transform, double Laplace transform, the projected differential transform method [16][17][18][19][20][21][22] and Adomian decomposition (ADM) method [23].…”

“…In this paper, we introduce an advanced method that relies on modified integral transform (MIT) [21], and one that uses simple techniques. Additionally, we contemplate the combination of MIT and the present technique to solve the B-L and SP-H equations [22].…”