The bi-Hamiltonian structure of original Hirota-Satsuma system proposed by Roy based on a modification of the bi-Hamiltonian structure of Ito system is incorrect.

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 2010 Elsevier Inc. All rights reserved.

In the first part of this work we study local well-posedness dispersive equations in weighted spaces $$H^s({\mathbb {R}})\cap L^2(|x|^{2b}dx)$$ . We then apply our results for several models such as Hirota-Satsuma system, OST equation, Kawahara equation and a fifth-order model. Using these results, second is devoted to obtain related blow up system.

We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV equation to other NPDEs. The method is based upon a linearization principle which can be applied on nonlinearities which have a polynomial form. We illustrate the ...

Collocation method using quintic B-splines finite element have been developed for solving numerically the HirotaSatsuma coupled MKdV equation. Accuracy of the proposed method is shown numerically by calculating conservation laws, 2 L and  L norms on studying of a soliton solution. It is shown that the collocation scheme for solutions of the MKdV equation gives rise to smaller errors and is qui...