相关论文: Uniqueness Properties of Solutions to Schr\"odinge…

We prove the existence of ground state solutions for the nonlinear Schrodinger-Maxwell equations with a singular potential.

We construct time quasi-periodic solutions to the energy supercritical nonlinear Schr\"odinger equations on the torus in arbitrary dimensions. This introduces a new approach, which could have general applicability.

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…

We show that formal Schr\"odinger operators with singular potentials from the space W^{-1}_{2,unif}(R) can be naturally defined to give selfadjoint and bounded below operators, which depend continuously in the uniform resolvent sense on the…

This paper is concerned with the numerical analysis of linear and nonlinear Schr{\"o}dinger equations with analytic potentials. While the regularity of the potential (and the source term when there is one) automatically conveys to the…

We consider the scattering transform for the Schr\"odinger equation with a singular potential and no bound states. Using the Riccati representation for real-valued potentials on the line, we obtain invertibility and Lipschitz continuity of…

In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong…

In this paper the one-dimensional nonparaxial nonlinear Schr\"odinger equation is considered. This was proposed as an alternative to the classical nonlinear Schr\"odinger equation in those situations where the assumption of paraxiality may…

We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…

Based on a method that produces the solutions to the Schrodinger equations of partner potentials, we give two conditionally exactly solvable partner potentials of exponential type defined on the half line. These potentials are…

We discuss the observability of a one-dimensional Schr\"odinger equation on certain time dependent domain. In linear moving case, we give the exact boundary and pointwise internal observability for arbitrary time. For the general moving, we…

We propose in this paper to study the solutions of some nonlinear elliptic equations with singular potential.

We consider the linear and non linear cubic Schr\"odinger equations with periodic boundary conditions, and their approximations by splitting methods. We prove that for a dense set of arbitrary small time steps, there exists numerical…

We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…

Various origins of linear and nonlinear Schrodinger equations are discussed in connection with diffusion, hydrodynamics, and fractal structure. The treatment is mainly expository, emphasizing the quantum potential, with a few new…

In this paper, we establish a Paley-Wiener type uncertainty principle for Schr\"odinger equations with bounded electric and magnetic potentials, \begin{align*} i\partial_tu+\Delta_Au+V(t,x)u=0,\,\,u(0,x)=u_0(x), \end{align*} where…

Motivated by the interest in non-relativistic quantum mechanics for determining exact solutions to the Schrodinger equation we give two potentials that are conditionally exactly solvable. The two potentials are partner potentials and we…

Using a new infinite-dimensional linking theorem, we obtained nontrivial solutions for strongly indefinite periodic Schr\"odinger equations with sign-changing nonlinearities.

The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a…

In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously…