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.