An irrational trial equation method and its applications

Abstract

An irrational trial equation method was proposed to solve nonlinear differential equations. By this method, a number of exact travelling wave solutions to the Burgers-KdV equation and the dissipative double sine-Gordon equation were obtained. A more general irrational trial equation method was discussed, and many exact solutions to the Fujimoto-Watanabe equation were given.

New solitary wave solutions of Maccari system

“…But if the solution is in terms of tanh function, soliton is called the dark soliton. In this work, we find some exact solutions such as soliton solutions, rational solutions, Jacobi elliptic function solutions and hyperbolic function solutions of Maccari system by using 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). These functions supply a system of differential equations.…”

New Exact Solutions of the Time-Fractional Nonlinear Dispersive KdV Equation

“…Some new trial equation methods were defined in literature [12]- [24]. In this paper, a new approach to the extended trial equation method will be given.…”

Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics

“…However, for some nonlinear ordinary differential equations with rank inhomogeneous, we cannot find a polynomial F(u) or a rational function F(u). Therefore, Du took F as an irrational function, and hence proposed a new trial equation method to solve these kinds of equations [27]. Also, Liu proposed a new version of the trial equation method which is suitable for nonlinear partial differential equations with variable coefficients [28].…”