Generalized Hasimoto transform of one-dimensional dispersive flows into compact Riemann surfaces.
Generalized Jacobi elliptic function solution to a class of nonlinear Schrödinger-type equations.
Geometric optics and instability for NLS and Davey-Stewartson models
We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with Gauge invariant power-law nonlinearities and nonlocal perturbations. The model includes the Davey-Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variants. Our analysis reveals a new localization phenomenon for nonlocal perturbations in the high frequency regime and allows us to infer strong instability results on the Cauchy problem in negative order Sobolev...
Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
Global controllability and stabilization for the nonlinear Schrödinger equation on an interval
We prove global internal controllability in large time for the nonlinear Schrödinger equation on a bounded interval with periodic, Dirichlet or Neumann conditions. Our strategy combines stabilization and local controllability near 0. We use Bourgain spaces to prove this result on L2. We also get a regularity result about the control if the data are assumed smoother.
Global dynamics beyond the ground state energy for nonlinear dispersive equations
This is a brief introduction to the joint work with Wilhelm Schlag and Joachim Krieger on the global dynamics for nonlinear dispersive equations with unstable ground states. We prove that the center-stable and the center-unstable manifolds of the ground state solitons separate the energy space by the dynamical property into the scattering and the blow-up regions, respectively in positive time and in negative time. The transverse intersection of the two manifolds yields nine sets of global dynamics,...
Global existence for a nonlinear Schroedinger–Chern–Simons system on a surface
Global existence of small classical solutions to nonlinear Schrödinger equations
Global existence of small radially symmetric solutions to quadratic nonlinear evolution equations in an exterior domain.
Global existence of solutions to Schrödinger equations on compact riemannian manifolds below
In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. , under some bilinear Strichartz assumption. We will find some , such that the solution is global for .
Global self-similar solutions of a class of nonlinear Schrödinger equations.
Global solutions with infinite energy for the one-dimensional Zakharov system.
Global well-posedness and scattering for the defocusing -subcritical Hartree equation in
Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
Global well-posedness and scattering for the higher-dimensional energy-critical nonlinear Schrödinger equation for radial data.
Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces.
Global well-posedness for the radial defocusing cubic wave equation on and for rough data.
Global well-posedness of NLS-KdV systems for periodic functions.
Global well-posedness of the Cauchy problem of a higher-order Schrödinger equation.
Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
We establish global existence and scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ¹ norm less than those of the ground state in , d ≥ 5.