A direct perturbation theory for solitons of the derivative nonlinear Schrödinger (DNLS) equation is developed based on a closure of eigenfunctions of the linearized DNLS equation around a one-soliton solution. The slow evolution of soliton parameters and the perturbation-induced radiation are obtained. Under the known simple gaugelike transformation, these results are transformed into those fo...

Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonline...

We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No–go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non– controllability for the linear Schrödinger equation and distributed additive control, a...

In this paper we use a similarity transformation connecting some families of Nonlinear Schrödinger equations with time-varying coefficients with the autonomous cubic nonlinear Schrödinger equation. This transformation allows one to apply all known results for that equation to the original non-autonomous case with the additional dynamics introduced by the transformation itself. In particular, us...

In this paper, a stochastic term is added to the classical generalized nonlinear Schrödinger Equation to describe the noise generated when light pulses propagate in a fiber. It has been shown that the generated supercontinuum light source fluctuates up to 50% of its output temporal intensity profile due to noises of different sources. The simulation method devised has been applied to the propag...

In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and three dimensions. The proposed method is based on a time-splitting method that decomposes the original problem into two parts, a linear equation and a nonlinear equation. The linear equation in one dimension is approximatedwith the Chebyshev pseudo-spectral collocationmethod in space variable and the Crank–...