Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation
H. Yépez-Martínez *
Autonomous University of Mexico City, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, P.O. Box 09790 México D.F., Mexico.
J. M. Reyes
Autonomous University of Mexico City, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, P.O. Box 09790 México D.F., Mexico.
I. O. Sosa
Autonomous University of Mexico City, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, P.O. Box 09790 México D.F., Mexico.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Fractional sub-equation method, Analytical solutions, Nonlinear KdV and mKdV fractional equations.