相关论文: Semiclassical Singularity Propagation Property for…

Soliton motion in some external potentials is studied using the nonlinear Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic…

We study the scattering behavior of global solutions to stochastic nonlinear Schr\"odinger equations with linear multiplicative noise. In the case where the quadratic variation of the noise is globally finite and the nonlinearity is…

We investigate the global well-posedness and modified scattering for the one-dimensional Schr\"odinger equation with gauge-invariant polynomial nonlinearity. For small localized initial data of finite energy in a low-regularity class, we…

Solutions of semi-classical Schrodinger equation with isotropic harmonic potential focus periodically in time. We study the perturbation of this equation by a nonlinear term. If the scaling of this perturbation is critical, each focus…

The numerical simulation of wave propagation in semiclassical (high-frequency) problems is well known to pose a formidable challenge. In this work, a new phase-space approach for the numerical simulation of semiclassical wave propagation,…

The small dispersion limit of the focusing nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. First, through a comprehensive set of numerical simulations, it is demonstrated that…

This work explores the non-relativistic quantum propagator $K(x,t)$ as a solution of the Schr\"odinger equation. We suppose that the propagator takes the form ${\rm exp}\left(\frac{\mathrm{i}}{\hbar}S+R\right)$, generalizing the usual WKB…

Conditional Lie symmetries of semi-linear 1D Schr\"odinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schr\"odinger…

We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…

In this paper we consider an initial/boundary value problem for the Schr\"odinger equation with a right-hand side involving the fractional Sturm-Liouville operator with singular propagation and potential. To construct a solution, first…

This paper is concerned with the final state problem for the homogeneous type nonlinear Schr\"odinger equation with time-decaying harmonic potential. The nonlinearity has the critical order and is not necessarily the form of a polynomial.…

A detailed exposition of highly efficient and accurate method for the propagation of the time-dependent Schr\"odinger equation is presented. The method is readily generalized to solve an arbitrary set of ODE's. The propagation is based on a…

We present several results concerning the semiclassical limit of the time dependent Schr\"odinger equation with potentials whose regularity doesn't guarantee the uniqueness of the underlying classical flow. Different topologies for the…

We investigate numerically by a conservative difference scheme in complex arithmetic the head-on and takeover collision dynamics of the solitary waves as solutions of linearly Coupled Nonlinear Schr\"odinger Equations for various initial…

For the $1+1$ dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the same way as the stochastic wave equation. This provides…

In this paper, we investigate the Schr\"odinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability. We illustrate that all…

We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…

In this paper we study the asymptotic behavior of a quadratic Schr\"{o}dinger equation with electromagnetic potentials. We prove that small solutions scatter. The proof builds on earlier work of the author for quadratic NLS with a non…

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…

We study the Schr\"odinger equation on a flat euclidean cone $\mathbb{R}_+ \times \mathbb{S}^1_\rho$ of cross-sectional radius $\rho > 0$, developing asymptotics for the fundamental solution both in the regime near the cone point and at…