1,000 research outputs found
A simple criterion of transverse linear instability for solitary waves
We prove an abstract instability result for an eigenvalue problem with
parameter. We apply this criterion to show the transverse linear instability of
solitary waves on various examples from mathematical physics.Comment: The main result has been improved and its proof simplifie
Small data scattering for the nonlinear Schr\"odinger equation on product spaces
We consider the cubic nonlinear Schr\"odinger equation, posed on , where is a compact Riemannian manifold and . We prove that
under a suitable smallness in Sobolev spaces condition on the data there exists
a unique global solution which scatters to a free solution for large times.Comment: 10 pages, slightly revised version, to appear on Comm. PD
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