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Minimizing the Ginzburg-Landau energy in a strip: (non-escaping) solitons and (escaping) solitonic vortices.

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DNMW06 - Recent challenges in the mathematical design of new materials

We study critical points of the Ginzburg-Landau energy on a 2D strip, related to the very experiments on fermionic condensates. In a recent work, Aftalion, Gravejat and Sandier showed that, as the width $d$ of the strip becomes larger than $\sqrt{2}\pi k/ 2$, there exists uniquely a local branch of critical points which bifurcate from the soliton, each of which has k vortices on a transverse line. Using instead a minimization procedure we establish the existence and uniqueness of these solutions for all $d > \sqrt{2}\pi k/ 2$. Time permitting, we also discuss related issues on a 3D cylinder. Joint work with Amandine Aftalion.

This talk is part of the Isaac Newton Institute Seminar Series series.

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