The improved F-expansion method and its applications

Soliton Soltuions of Nonlinear Evolutions Equation by using the Extended Exp (-φ(ξ)) Expansion Method

“…Recently, many solutions methods have been introduced to get the exact solutions of NLPDEs. For example, extended Jacobian Elliptic Function Expansion Method [2], the modified simple equation method [3], the tanh method [4], extended tanh -method [5]- [7], sine -cosine method [8]- [10], homogeneous balance method [11,12],F-expansion method [13]- [15], exp-function method [16,17], trigonometric function series method [18], ( [19]- [22], Jacobi elliptic function method [23]- [26], The exp(−ϕ(ξ))-expansion method [27]- [29] and so on. In this article we propose a new method to get the exact traveling wave solutions and the solitary wave solutions of the (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equatio which is a widely used model for investigation the dynamics of solitons and nonlinear wave in areas such as fluid dynamics, plasma physics and weakly dispersive media by using the extended exp(−ϕ(ξ))-expansion method.…”

The exp(-φ(ξ))-Expansion Method and Its Application for Solving Nonlinear Evolution Equations

“…Exact solutions for these equations play an important role in many phenomena in physics such as uid mechanics, hydrodynamics, optics, plasma physics and so on. Recently many new approaches for finding these solutions have been proposed, for example, extended Jacobian Elliptic Function Expansion Method [2], the modified simple equation method [3], the tanh method [4], extended tended tanh-method [5]- [7], sine-cosine method [8]- [10], homogeneous balance method [11] [12], F-expansion method [13]- [15], exp-function method [16] [17], trigonometric function series method [18], G G ′       -expansion method [19]- [22], Jacobi elliptic function method [23]- [26], the exp ( ) ( ) ϕ ξ − -expansion method [27]- [29] and so on.…”

The exp<span style="font-family:Symbol;font-size:11pt;">(-j(x))</span> Method and Its Applications for Solving Some Nonlinear Evolution Equations in Mathematical Physics

“…Exact solutions for these equations play an important role in many phenomena in physics such as fluid mechanics, hydrodynamics, Optics, Plasma physics and so on. Recently many new approaches for finding these solutions have been proposed, for example, tanh-sech method [2]- [4], extended tanh-method [5], extended jacobain method [6], modified simple equation method [7] [8], sine-cosine method [9] [10], homogeneous balance method [11] [12], F-expansion method [13]- [15], exp-function method [16] [17], trigonometric function series method [18], G G ′       -expansion method [19]- [22], Jacobi elliptic function method [23]- [26], the ( ) ( ) ( )…”