Modified Trial Equation Method to the Nonlinear Fractional Sharma–Tasso–Olever Equation

Abstract

Abstract-In this paper, we apply the modified trial equation method to fractional partial differential equations. The fractional partial differential equation can be converted into the nonlinear non-fractional ordinary differential equation by the fractional derivative and traveling wave transformation. So, we get some traveling wave solutions to the time-fractional Sharma-Tasso-Olever (STO) equation by the using of the complete discrimination system for polynomial method. The acquired results can be demoted by the soliton solutions, single-king solution, rational function solutions and periodic solutions.Index Terms-The modified trial equation method, fractional Sharma-Tasso-Olever equation, soliton solution, periodic solutions.

New solitary wave solutions of Maccari system

“…Our purpose in this paper is to obtain exact solutions of Maccari system. In Section 2, we give the fundamentals of extended trial equation method (Liu, 2005;Du, 2010;Pandir et al, 2012;Pandir and Gurefe, 2013;Pandir et al, 2013a,b,c;Gurefe et al, 2013;Bulut et al, 2013a,b;Bulut and Pandir 2013;Bulut et al, 2014b;Bulut, 2013;Liu, 2013;Pandir, 2014b;Demiray and Bulut, 2015). In Section 3, we give the fundamentals of generalized Kudryashov method.…”

The analysis of the exact solutions of the space fractional coupled KD equations

“…Exact solutions of fractional differantial equations has been investigated by using a lot of methods such as the extended trial equation method [9,10,11], the modified trial equation method [13,14,12], a multiple extended trial equation method [15] and the modified kudryashov method [16,18].…”

Exact solutions of nonlinear Schrodinger’s equation with dual power-law nonlinearity by extended trial equation method

“…In recent years, most authors have improved a lot of methods to find exact solutions of NLEEs such as G'/G-expansion method [8][9][10], exp-function method [11][12], the tanh method [13], homogeneous balance method [14], and many more. In this paper, the extended trial equation method [15][16][17][18][19][20][21][22][23][24][25][26][27] will be applied to obtain exact solutions to the NLSE. Finally, we can say that the obtained solutions satisfy the equation.…”