Related papers: Microlocal smoothing effect for the Schr\"odinger …
A recent area of interest is the development and study of eigenvalue problems arising in scattering theory that may provide potential target signatures for use in nondestructive testing of materials. We consider a generalization of the…
We establish dispersive estimates and local decay estimates for the time evolution of non-self-adjoint matrix Schr\"odinger operators with threshold resonances in one space dimension. In particular, we show that the decay rates in the…
A new decomposition for frequency-localized solutions to the Schrodinger equation is given which describes the evolution of the wavefunction using a weighted sum of Lipschitz tubes. As an application of this decomposition, we provide a new…
In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schr\"odinger…
Found are conditions on a scalar type spectral operator $A$ in a complex Banach space necessary and sufficient for all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\ t\ge 0, \end{equation*} to be strongly Gevrey…
In this article, we analyze the propagation of Wigner measures of a family of solutions to a system of semi-classical pseudodifferential equations presenting eigenvalues crossings on hypersurfaces. We prove the propagation along classical…
We consider perturbations of the semiclassical Schr{\"o}dinger equation on a compact Riemannian surface with constant negative curvature and without boundary. We show that, for scales of times which are logarithmic in the size of the…
A nonlinear evolution equation for wave packet surface gravity waves with variation in topography is revisited in this article. The equation is modeled by a spatial inhomogeneous nonlinear Schr\"odinger (NLS) equation with varying…
In this paper we analyze the dispersion for one dimensional wave and Schrodinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the coefficient…
We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schr\"odinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are…
A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. This dispersion is associated with the continuous spectrum of…
In this paper, we investigate quantitative propagation of smallness properties for the Schr\"odinger operator on a bounded domain in $\mathbb R^d$. We extend Logunov, Malinnikova's results concerning propagation of smallness for…
We prove the equivalence between the smoothing effect for a Schr\"odinger operator and the decay of the associate spectral projectors. We give two applications to the Schr\"odinger operator in dimension one.
Nonlocal nonlinear Schroedinger-type equation is derived as a model to describe paraxial light propagation in nonlinear media with different `degrees' of nonlocality. High frequency limit of this equation is studied under specific…
In this paper we prove local well-posedness of a space-time fractional generalization of the nonlinear Schr\"odinger equation with a power-type nonlinearity. The linear equation coincides with a model proposed by Naber, and displays a…
An understanding of the long-term evolution of self-gravitating disks ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disk,…
Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We prove smoothing properties along suitable directions of the Ornstein-Uhlenbeck evolution operator, namely the evolution operator associated to non autonomous Ornstein-Uhlenbeck equations. Moreover we use such smoothing estimates to prove…