We present the results of further analysis of the integrability properties of the N = 4 supersymmetric KdV equation deduced earlier by two of us (F.D. & E.I., Phys. Lett. B 309 (1993) 312) as a hamiltonian flow on N = 4 SU(2) superconformal algebra in the harmonic N = 4 superspace. To make this equation and the relevant hamiltonian structures more tractable, we reformulate it in the ordinary N ...

In this paper we obtain one and two soliton solutions to HirotaSatsuma KdV system with the aid of Hirota’s bilinear method. We also obtain some rational solutions. Mathematics Subject Classification: 35C05

We study the traveling waves of the Nonlinear Schrödinger Equation in dimension one. Through various model cases, we show that for nonlinearities having the same qualitative behaviour as the standard Gross-Pitaevkii one, the traveling waves may have rather different properties. In particular, our examples exhibit multiplicity or nonexistence results, cusps (as for the Jones-Roberts curve in the...

This paper studies the problem of optimal control of the viscous KdV-Burgers’ equation. We develop a technique to utilize the Cole-Hopf transformation to solve an optimal control problem for the viscous KdV-Burgers’ equation. While the viscous KdV-Burgers’ equation is transformed into a simpler linear equation, the performance index is transformed to a complicated rational expression. We show t...

Based on estimates for the KdV equation in analytic Gevrey classes, a spectral collocation approximation of the KdV equation is proved to converge exponentially fast. Mathematics Subject Classification. 35Q53, 65M12, 65M70. Received: March 31, 2006. Revised: July 11, 2006.

In this study, the generalized coupled nonlinear Schrödinger–KdV (NLS–KdV) system is investigated to obtain new optical soliton solutions. This appears as a model for reciprocity between long and short waves in various physical settings. Different kinds of solutions including dark, bright, combined dark-bright, singular are obtained using two effective methods namely, extended sinh–Gordon equat...