Curve concentration for 2D nonlinear Schrödinger equations with a finite magnetic potential

This paper concerns the two-dimensional nonlinear Schrödinger equation with a strong coupling between electromagnetic potentials. Along a sequence of semiclassical parameters ε_n→0, we construct complex-valued solutions that concentrate on a closed smooth curve. The location of this concentration curve is determined jointly by the electric potential and the magnetic potential. Notably, the influence of the magnetic field is inherently nonlocal. To the best of our knowledge, this is the first result demonstrating the influence of the magnetic potential on concentration phenomena in dimensions greater than one without imposing any symmetry assumptions.