Abstract
ABSTRACTIn the present paper, expansion method is applied to the space-time fractional third order Korteweg-De Vries (KdV) equation, space-time fractional Caudrey-Dodd-Gibbon (CDG) equation, space-time fractional (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation and space-time fractional (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) equation. Here, the fractional derivatives are described in conformable sense. The obtained traveling wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. The graphs for some of these solutions have been presented by choosing suitable values of parameters to visualize the mechanism of the given nonlinear fractional evolution equations.
Highlights
The nonlinear evolution equations are widely used as models to describe complex physical phenomena in various field of science, in fluid mechanics, solid state physics, plasma waves and chemical physics
Natural transform and Homotopy perturbation methods, Homotopy Perturbation Transform Method, Riccati Equation Approach, extended hyperbolic function method, projective Riccati equation method and the Exp-function method have been applied to the third order KDV equation in [6,7,8,9,10]
Jacobi elliptic function expansion method has been applied to conformable space-fractional Korteweg-De Vries (KdV) equation in [11]
Summary
The nonlinear evolution equations are widely used as models to describe complex physical phenomena in various field of science, in fluid mechanics, solid state physics, plasma waves and chemical physics (see, for example, [1,2,3,4]). We apply G /G2 expansion method (see, for example, [5]) to four space-time fractional nonlinear evolution equations: space-time fractional third-order KdV equation, space-time fractional CDG equation, space-time fractional (2+1)-dimensional CBS equation and space-time fractional (2+1)-dimensional AKNS equation. The sin-cosine method, the rational Exp-Function, sinh method, G /G-expansion method, Hirota’s bilinear method and exp-function method have been used to obtain solutions of the fifth order CDG equation in [12,13,14]. Hirota’s bilinear method, TANF(ξ/2)expansion method, the ansatz method, the improved tanh method, the simplified form of the bilinear method to obtain some new exact solutions for high nonlinear form of (2+1)-dimensional AKNS equation have been presented in [24,25,26,27,28]. Bilinear Backlund transformation has been presented to obtain periodic wave solutions of (2+1)-dimensional AKNS equation in [29]
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