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A generic framework of adiabatic approximation for nonlinear evolutions II
Jingxuan Zhang
In this paper, we continue the development of a generic adiabatic scheme for nonlinear evolutions. We consider an abstract gradient flow of some energy functional, together with a…
Ginzburg-Landau Equations on Non-compact Riemann Surfaces
Nicolas M. Ercolani, Israel Michael Sigal, Jingxuan Zhang
We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less…
Adiabatic approximation for the motion of Ginzburg-Landau vortex filament
Jingxuan Zhang
In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has…
A generic framework of adiabatic approximation for evolutions with focusing nonlinearity
Jingxuan Zhang
In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dim…