Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation
H. Yépez-Martínez, J. M. Reyes, I. O. Sosa
Journal of Advances in Mathematics and Computer Science · pp. 572–589 · Published 21 Nov 2013
10.9734/BJMCS/2014/7059Abstract
The fractional sub-equation method is proposed to construct analytical solutions of nonlinear fractional partial differential equations (FPDEs), involving Jumarie’s modified Riemann-Liouville derivative. The fractional sub-equation method is applied to the space-time fractional generalized Hirota-Satsuma coupled KdV equation and coupled mKdV equation. The analytical solutions show that the fractional sub-equation method is very effective for the fractional coupled KdV and mKdV equations. The solutions are compared with that of the extended tanh-function method. New exact solutions are found for the coupled mKdV equation.
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