相关论文: On the Integrability of the Discrete Nonlinear Sch…

A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…

An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can…

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability…

In this paper we deal with a nonlinear Schr\"{o}dinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time…

A recently proposed discrete version of the Schrodinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated to this spectral problem is derived. It is shown that a discrete…

The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…

We consider the relation between the discrete coupled nonlinear Schr\"{o}dinger equation and Toda equation. Introducing complex times we can show the intergability of the discrete coupled nonlinear Schr\"{o}dinger equation. In the same way…

A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in…

In this paper we derive the Schroedinger equation by assuming it describes the time evolution of a deterministic and reversible process that leaves at each moment in time a different observable well defined; that is, it allows an accurate…

We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…

A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical…

In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…

In this article we prove a reducibility result for the linear Schr\"odinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less or equal than $1/2$. As far as we know, this is the first…

An effective equation describes a weakly nonlinear wave field evolution governed by nonlinear dispersive PDEs \emph{via} the set of its resonances in an arbitrary big but finite domain in the Fourier space. We consider the Schr\"{o}dinger…

We analize the Nonlinear Schr\"odinger Equation.

We consider the problem of reflectionless propagation of PT-symmetric solitons described by the nonlocal nonlinear Schroedinger equation on a line in the framework of the concept of transparent boundary conditions for evolution equations.…

We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…

The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The…

It is shown that Schroedinger equation is not consistent with information theory. From the modified form of information which ensures that the most probable density function it yields tallies with a general form of continuous Riemann…

We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely…