Two novel modifications of the exp-function method have been suggested to solve nonlinear system partial differential equation fractional order for first time. The fractional-order Hirota-Satsuma coupled KdV has solved precisely; as a result, some exact solutions, which include soliton-type and rational will be derived. Eventually, graphs obtained results illustrated at end article. newly used ...

Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian’s decomposition method (ADM) and homotopy perturbation method (HPM), has led us to s...

Abstract: In this paper, the homotopy perturbation method (HPM) is applied to obtain approximate solutions to three systems of nonlinear wave equations, namely, two component evolutionary system of a homogeneous KdV equations of order 3 (type I) as well as (type II), and the generalized coupled Hirota Satsuma KdV. The numerical results show that this method is a powerful tool for solving system...

We show a surprising connection between known integrable Hamiltonian systems with quartic potential and the stationary flows of some coupled KdV systems related to fourth order Lax operators. In particular, we present a connection between the Hirota-Satsuma coupled KdV system and (a generalisation of) the 1 : 6 : 1 integrable case quartic potential. A generalisation of the 1 : 6 : 8 case is sim...

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense ofmodified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled...

In this paper, we study the generalized coupled Hirota–Satsuma KdV system by using the two new improved projective Riccati equations method. As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and combined formal solitary wave solutions and combined formal periodic wave solutions are obtained. c © 2007 Published by Elsevier Ltd