Gang, Zhou; Weinstein, Michael I. Dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations: mass transfer in systems with solitons and degenerate neutral modes. (English) Zbl 1175.35136 Anal. PDE 1, No. 3, 267-322 (2008). The authors prove the asymptotic stability of the ground state of NLS/GP equation when the linearized spectrum has degenerate neutral modes. They show that the solution has three interacting parts: i) a modulating soliton, parametrized by the motion along ground state; ii) oscillatory, spacially localized, neutral modes, which decay with time; iii) a dispersive part, which decays in a local energy norm. The neutral modes and dispersive waves decay via transferring their mass to the soliton manifold or to spatial infinity. Additionally, degenerate neutral modes are coupled and exchange mass among themselves in addtition to with the soliton and radiation. Reviewer: Igor Andrianov (Köln) Cited in 19 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35B35 Stability in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems 35C08 Soliton solutions Keywords:soliton; nonlinear bound state; nonlinear scattering; asymptotic stability; dispersive PDE PDF BibTeX XML Cite \textit{Z. Gang} and \textit{M. I. Weinstein}, Anal. PDE 1, No. 3, 267--322 (2008; Zbl 1175.35136) Full Text: DOI arXiv Link OpenURL