2024/08/15 by John Albert, Albert, John, Jack Arbunich +1
Mathematics · #35B35 (Secondary) #35Q55 (Primary) 35Q60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2408.08279
openalex publication_date 2024/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the stability of bound-state solutions of a family of regularized nonlinear Schrödinger equations which were introduced by Dumas, Lannes and Szeftel as models for the propagation of laser beams. Among these bound-state solutions are ground states, which are defined as solutions of a variational problem. We give a sufficient condition for existence and orbital stability of ground states, and use it to verify that ground states exist and are stable over a wider range of nonlinearities than for the nonregularized nonlinear Schrödinger equation. We also give another sufficient and almost necessary condition for stability of general bound states, and show that some stable bound states exist which are not ground states.