We consider the derivative nonlinear Schrodinger equation in one space dimension, posed both on line and circle. This model is known to be completely integrable $L^2$-critical with respect scaling. The first question we discuss whether ensembles of orbits $L^2$-equicontinuous initial data remain equicontinuous under evolution. prove that this true restriction $M(q)=\int |q|^2 < 4\pi$. conject...

— In this paper we construct a Gibbs measure for the derivative Schrödinger equation on the circle. The construction uses some renormalisations of Gaussian series and Wiener chaos estimates, ideas which have already been used by the second author in a work on the Benjamin-Ono equation.

we consider a new type of integrable coupled nonlinear schrodinger (cnls)equations proposed by our self [submitted to phys. plasmas (2011)]. the explicitform of soliton solutions are derived using the hirota&apos;s bilinear method.we show that the parameters in the cnls equations only determine the regionsfor the existence of bright and dark soliton solutions. finally, throughthe linear stabili...