Andres Contreras

L2 orbital stability of Dirac solitons in the massive Thirring model

ABSTRACT We prove L2 orbital stability of Dirac solitons in the massive Thirring model. Our method uses local well posedness of the massive Thirring model in L2, conservation of the charge functional, and the auto–Bäcklund transformation. The latter transformation exists because the massive Thirring model is integrable via the inverse scattering transform method.

Domain Walls in the Coupled Gross–Pitaevskii Equations

A thorough study of domain wall solutions in coupled Gross–Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear stability; their persistence and stability under a small localized potential. The proof of existence is variational and is presented in a general framework: we show that the domain wall solutions are energy minimizers within a class of vector-valued functions with nontrivial conditions at infinity. The admissible energy functionals include those corresponding to coupled Gross–Pitaevskii equations, arising in modeling of Bose–Einstein condensates. The results on spectral and nonlinear stability follow from properties of the linearized operator about the domain wall. The methods apply to many systems of interest and integrability is not germane to our analysis. Finally, sufficient conditions for persistence and stability of domain wall solutions are obtained to show that stable pinning occurs near maxima of the potential, thus giving rigorous justification to earlier results in the physics literature.

Stability of multi-solitons in the cubic NLS equation

We address the stability of multi-solitons for the cubic nonlinear Schrodinger (NLS) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we establish the orbital stability of multi-solitons in the L2(ℝ) space when the initial data is in a weighted L2(ℝ) space.

Persistence of superconductivity in thin shells beyond Hc1

In Ginzburg-Landau theory, a strong magnetic field is responsible for the breakdown of superconductivity. This work is concerned with the identification of the region where superconductivity persists, in a thin shell superconductor modeled by a compact surface

Nearly Parallel Vortex Filaments in the 3D Ginzburg–Landau Equations

\mathcal M\subset\mathbb R^3

Orbital Stability of Domain Walls in Coupled Gross--Pitaevskii Systems

, as the intensity

Gamma-convergence and the emergence of vortices for Ginzburg–Landau on thin shells and manifolds

h

Biaxial escape in nematics at low temperature

of the external magnetic field is raised above

Nodal bubble-tower solutions to radial elliptic problems near criticality

H_{c1}

On the First Critical Field in Ginzburg–Landau Theory for Thin Shells and Manifolds

. Using a mean field reduction approach devised by Sandier and Serfaty as the Ginzburg-Landau parameter