Rigorous numerics for NLS: bound states, spectra, and controllability

2013/10/24 by Roberto Castelli, Castelli, Roberto, Holger Teismann +1
Mathematics · Physics and Astronomy · #35Q55 #35Q93 #65G99 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DS #math.MP #msc:35Q55 #msc:35Q93 #msc:65G99

paper · pdf · doi:10.48550/arxiv.1310.6531

30 pages, 2 figures

arxiv created 2013/10/24 · arxiv updated 2013/10/25

Abstract

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS.

Related

• Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions
• Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control
• Controllability of NLS in the vicinity of solitary wave solutions
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• Stability of exact solutions of the (2+1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ