相关论文: Integrable Nonautonomous Nonlinear Schrodinger Equ…

We introduce a new non-resonant low-regularity integrator for the cubic nonlinear Schr\"odinger equation (NLSE) allowing for long-time error estimates which are optimal in the sense of the underlying PDE. The main idea thereby lies in…

After performing the Madelung transformation, the nonlinear Schr\"odinger equation is transformed into a hydrodynamic equation akin to the compressible Euler equations with a certain dissipation. In this short note, we construct…

We examine a recently-proposed family of nonlinear Schr\"odinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamily of them. We investigate the structure of the whole…

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…

We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…

This work is devoted to an integrable generalization of the nonlinear Schr\"odinger equation proposed by Fokas and Lenells. I discuss the relationships between this equation and other integrable models. Using the reduction of the…

In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schr\"odinger equation, which is widely used in fiber-optic communications. The landscape and minimizers of the…

The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated…

Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…

By using AKNS scheme and soliton connection taking values in a Virasoro algebra we obtain new coupled Nonlinear Schrodinger equations.

The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…

We apply Painlev\'e test to the most general variable coefficient nonlinear Schrodinger (VCNLS) equations as an attempt to identify integrable classes and compare our results versus those obtained by the use of other tools like…

In the present contribution we consider a class of Schroedinger equations containing complex nonlinearities, describing systems with conserved norm $|\psi|^2$ and minimally coupled to an abelian gauge field. We introduce a nonlinear…

We prove new local and global well-posedness results for the cubic one-dimensional nonlinear Schr\"odinger equation in modulation spaces. Local results are obtained via multilinear interpolation. Global results are proven using conserved…

In this paper, we investigate the damped stochastic nonlinear Schr\"odinger(NLS) equation with multiplicative noise and its splitting-based approximation. When the damped effect is large enough, we prove that the solutions of the damped…

We study two integrable systems associated with the coupled NLS equation: the integrable defect system and the integrable boundary systems. Regarding the first one, we present a type I defect condition, which is described by a B\"{a}cklund…

We have studied the discrete nonlinear Schroedinger equation (DNLSE) with on-site defects and periodic boundary conditions. When the array dynamics becomes chaotic, the otherwise quasiperiodic amplitude correlations between the oscillators…

We obtain a self-dual formulation of the conventional nonlinear Schr\"odinger equation (NLSE) in the 1+1 dimension by studying the dimensional reduction of the self-dual Chern-Simons nonlinear Schr\"odinger model (NLSM) in the 2+1…

Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schr\"odinger equation (NLSE) originally discovered by Calogero,…

We derive an exact solution to the local nonlinear Schr\"odinger equation (NLSE) using the Darboux transformation method. The new solution describes the profile and dynamics of a two-soliton molecule. Using an algebraically-decaying seed…