On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions.
On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case
On the NLS dynamics for infinite energy vortex configurations on the plane.
On the number of single-peak solutions of the nonlinear Schrödinger equation
On the one class of hyperbolic systems.
On the real analyticity of the scattering operator for the Hartree equation
We study the real analyticity of the scattering operator for the Hartree equation . To this end, we exploit interior and exterior cut-off in time and space, together with a compactness argument to overcome difficulties which arise from absence of good properties as for the Klein-Gordon equation, such as the finite speed of propagation and ideal time decay estimate. Additionally, the method in this paper allows us to simplify the proof of analyticity of the scattering operator for the nonlinear...
On the rigidity of minimal mass solutions to the focusing mass-critical NLS for rough initial data.
On the scattering in Gevrey classes for the subcritical Hartree and Schrödinger equations
On the Virasoro structure of symmetry algebras of nonlinear partial differential equations.
On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
On two-dimensional finite-gap potential Schrödinger and Dirac operators with singular spectral curves.
Optical vortices in dispersive nonlinear Kerr-type media.
Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...
Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential.