Multiple normalized solutions to a system of nonlinear Schrödinger equations.

Abstract:  We present recent results concerning normalized solutions to a system of coupled nonlinear Schr¨odinger equations. The problem appears in different areas of mathematical physics, e.g. in the analysis of Bose-Einstein condensation or in nonlinear optics. By means of spectral results, the Cwikel-Lieb-Rozenblum theorem, the Morse index and new Liouville-type results we show the existence of multiple normalized solutions for sufficiently large coupling. The talk is based on joint work with Andrzej Szulkin.

Posted on Jan 21, 2025 in Differential Equations, Seminars