The Double (G^( ^' )/G,1/G)-Expansion Method and Its Applications for Some Nonlinear Partial Differential Equations

Abstract

The double (G^( ^' )/G,1/G)-expansion method is used to find exact travelling wave solutions to the fractional differantial equations in the sense of Jumarie’s modified Riemann- Liouville derivative. We exploit this method for the combined KdV- negative-order KdV equation (KdV-nKdV) and the Calogero-Bogoyavlinskii-Schiff equation (CBS) of fractional order. We see that these solutions are concise and easy to understand the physical phenomena of the nonlinear partial differential equations. These solutions can be shown in terms of trigonometric, hyperbolic and rational functions.

Keywords

• The double expansion method
• the Calogero–Bogoyavlinskii–Schiff equation
• the combined KdV- negative-order KdV equation

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