A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlevé analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.

In this paper, we explore the travelling wave solutions for some nonlinear partial differential equations by using recently established rational (G' /G)-expansion method. We apply method to combined KdV-mKdV equation, reaction-diffusion equation and coupled Hirota-Satsuma KdV equations. The are expressed hyperbolic functions, trigonometric functions functions. When parameters taken as special v...

In this work, we take Adomian Decomposition Method (ADM) and combine it with Sumudu Transform method (STM). This connection between the two methods is called Sumudu-Decomposition (SDM), then use to solve generalized Hirota-Satsuma Coupled kdv (H-SC kdv) systems also applied STM, find approximate solutions of system one. Then compare way exact solitary solutions. Clarifying best through tables d...

In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

In the paper, with the aid of symbolic computation, we investigate the generalized Hirota–Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of newWeierstrass elliptic function solutions via Weierstrass elliptic function }(n...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.