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 ...

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...

In this paper, a new space-time spectral algorithm is constructed to solve the generalized Hirota-Satsuma coupled Korteweg-de Vries (GHS-C-KdV) system of time-fractional order. The present algorithm consists of applying the collocationspectral method in conjunction with the operational matrix of fractional derivative for the double Jacobi polynomials, which will be employed as a basis function ...

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...

On the exact solutions of integrable models, there is a new classification way recently based on the property of associated spectral parameters [1]. Negatons, related to the negative spectral parameter, are usually expressed by hyperbolic functions, and positons are expressed by means of trigonometric functions related to the positive spectral parameters. The so-called complexiton, which is exp...