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Semiclassical limit for generalized KdV equations before the gradient catastrophe
Semiclassical limit generalized KdV equations the gradient catastrophe Analysis of PDEs
2011/8/24
Abstract: We study the semiclassical limit of the (generalised) KdV equation, for initial data with Sobolev regularity, before the time of the gradient catastrophe of the limit conservation law. In pa...
The semiclassical limit of focusing NLS for a family of non-analytic initial data
semiclassical limit non-analytic initial data NLS
2011/7/7
The small dispersion limit of the focusing nonlinear Schro\"odinger equation (NLS) exhibits a rich structure of sharply separated regions exhibiting disparate rapid oscillations at microscopic scales....
Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains
Klein Gordon Equation Semiclassical Limit Variational Methods Nonlinear Equations
2011/2/28
We are interested to the existence of standing waves for the nonlinear Klein Gordon equation "2 + W′( ) = 0 in a bounded domain D.
Semiclassical limit for mixed states with singular and rough potentials
Semiclassical limit for mixed states singular rough potentials
2011/1/20
We consider the semiclassical limit for the Heisenberg-von Neumann equation with a potential which consists of the sum of a repulsive Coulomb potential, plus a Lipschitz po-tential whose gradient belo...
A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit
Virial theorem semiclassical limit classically forbidden region
2010/12/1
We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant ~ ! 0. Proofs of these results rely on the genera...
The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited
he semiclassical limit of eigenfunctions Schrö dinger equation Bohr-Sommerfeld quantization condition
2010/12/1
Consider the semiclassical limit, as the Planck constant ~ ! 0, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions an...
Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain
Semiclassical Limit Gross-Pitaevskii Equation Exterior Domain
2018/4/20
In this paper, we study the semiclassical limit of the Gross-Pitaevskii equation (a cubic nonlinear Schrodinger quation) with the Neumann boundary condition in an exterior domain. We prove that befor...
Semiclassical limit for the Schroedinger equation with a short scale periodic potential
Semiclassical limit for the Schroedinger equation short scale periodic potential
2010/11/2
We consider the dynamics generated by the Schroedinger operator $H=-{1/2}\Delta + V(x) + W(\epsi x)$, where $V$ is a lattice periodic potential and $W$ an external potential which varies slowly on the...