2009/06/01 by Jeremy L. Marzuola, Jeremy Marzuola, Marzuola, Jeremy
Mathematics · Physics and Astronomy · #35B35 #35Q51 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Class (philosophy) #Combinatorics #Dimension (graph theory) #FOS: Mathematics #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Physics #Quantum mechanics #Soliton #Subspace topology #math.AP #msc:35B35 #msc:35Q51
paper · pdf · doi:10.48550/arxiv.0906.0375
published in arXiv (Cornell University) (Cornell University) · 22 pages, 1 figure
openalex publication_date 2009/06/01 · arxiv created 2009/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this result, we develop the techniques of \citeKS1 and \citeBW in order to determine a class of stable perturbations for a minimal mass soliton solution of a saturated, focusing nonlinear Schrödinger equation c i ut + Δu + β(|u|2) u = 0 u(0,x) = u0 (x), in \reals3. By projecting into a subspace of the continuous spectrum of H as in \citeS1, \citeKS1, we are able to use a contraction mapping similar to that from \citeBW in order to show that there exist solutions of the form e^i λmin t (Rmin + ei H t ϕ+ w(x,t)), where ei H t ϕ+ w(x,t) disperses as t → ∞. Hence, we have long time persistance of a soliton of minimal mass despite the fact that these solutions are shown to be nonlinearly unstable in \citeCP1.