Vortex Dynamics for the Ginzburg-Landau-Schrödinger Equation
| dc.creator | Colliander, James Ellis | |
| dc.creator | Jerrard, Robert L. | |
| dc.date | 1997-12-12 | |
| dc.date.accessioned | 2026-07-07T10:15:46Z | |
| dc.date.available | 2026-07-07T10:15:46Z | |
| dc.description | The initial value problem for the Ginzburg-Landau-Schrödinger equation is examined in the $ε\rightarrow 0$ limit under two main assumptions on the initial data $ϕ^ε$. The first assumption is that $ϕ^ε$ exhibits $m$ distinct vortices of degree $\pm 1$; these are described as points of concentration of the Jacobian $[Jϕ^ε]$ of $ϕ^ε$. Second, we assume energy bounds consistent with vortices at the points of concentration. Under these assumptions, we identify ``vortex structures'' in the $ε\rightarrow 0$ limit of $ϕ^ε$ and show that these structures persist in the solution $u^ε(t)$ of $GLS_ε$. We derive ordinary differential equations which govern the motion of the vortices in the $ε\rightarrow 0$ limit. The limiting system of ordinary differential equations is a Hamitonian flow governed by the renormalized energy of Bethuel, Brezis and Hélein. Our arguments rely on results about the structural stability of vortices which are proved in a separate paper. | |
| dc.identifier | https://arxiv.org/abs/math/9712278 | |
| dc.identifier | http://arxiv.org/abs/math/9712278 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173286 | |
| dc.subject | Mathematical Physics | |
| dc.title | Vortex Dynamics for the Ginzburg-Landau-Schrödinger Equation | |
| dc.type | text |