In this Letter we introduce a systematic perturbation method for analyzing the eeect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrr odinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpliied, depending on whether PNLS is power conserving...

We review a variety of recently obtained trace formulas for one-and multi-dimensional Schrr odinger operators. Some of the results are extended to Sturm-Liouville and matrix-valued Schrr odinger operators. Furthermore, we recall a set of trace formulas in one, two, and three dimensions related to point interactions as well as a new uniqueness result for three-dimensional Schrr odinger operators...

We consider models of random Schrr odinger operators which exist thanks to a cohomological theorem in ergodic theory. Examples are ergodic Schrr odinger operators with random magnetic uxes on discrete two-dimensional lattices or non-periodic situations like Penrose lattices.

In this paper, we present exact N-soliton solution by employing simple, straightforward Darboux transformation based on the Lax pair for Hirota equation, a higher-order nonlinear Schr€ odinger (HNLS) equation. As examples, oneand two-soliton solutions in explicit forms are given and their properties are also analyzed. A bound solution without interaction will be theoretically predicted if one c...

Light-front holographic QCD provides a successful first approximation to hadron spectroscopy in the chiral limit of ($3+1$)-dim light-front QCD, where Schr\"odinger-like equation, with an emerging confining scale, $\ensuremath{\kappa}$, governs confinement transverse direction. In its supersymmetric formulation, holography predicts that each baryon has two superpartners: meson and tetraquark, t...

In the present work, employing a one dimensional model of an unmagnetized collisionless plasma consisting of a cold electron fluid, hot electrons obeying j velocity distribution, and stationary ions, we study the amplitude modulation of an electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations of such a plasma, we obtained the nonlinear S...

Feynman has shown that a closed, locally interacting quantum system is capable of performing deterministic computation. For two nite-size versions of such a computer, the Schrr odinger equations are solved analytically. The probability that the computer yields a nal result upon measurement is derived.

We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem of operators with no term are presented and proved. The solution is expressed in quasideterminant forms. Additionally, parabolic soliton solutions equation given as explicit examples.

The authors show the disintegration of a higher-order rogue wave solution nonlinear Schr\odinger equation into its constituent parts in presence system perturbation.

In this paper, we implement the Adaptive Moving Mesh method (AMM) to solution of initial value problems involving Schr\"odinger equation, and more specifically Schr\"odinger-Poisson system equations. This is based on problem a discrete domain, whose resolution coordinate time-dependent, allows dynamically assign numerical in terms desired refinement criteria. We apply solve various test station...