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DOE OSTI · 21501296

Embedded eigenvalues and the nonlinear Schroedinger equation

Asad, R·Simpson, G
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Abstract

A common challenge in proving asymptotic stability of solitary waves is understanding the spectrum of the operator associated with the linearized flow. The existence of eigenvalues can inhibit the dispersive estimates key to proving stability. Following the work of Marzuola and Simpson [Nonlinearity 52, 389 (2011)], we prove the absence of embedded eigenvalues for a collection of nonlinear Schroedinger equations, including some one and three dimensional supercritical equations, and the three dimensional cubic-quintic equation. Our results also rule out nonzero eigenvalues within the spectral gap and end point resonances. The proof is computer assisted as it depends on the signs of certain inner products which do not readily admit analytic representations. Our source code is available for verification at http://hdl.handle.net/1807/26121.

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97 MATHEMATICS AND COMPUTINGASYMPTOTIC SOLUTIONSDIFFERENTIAL EQUATIONSEIGENFUNCTIONSEIGENVALUESEQUATIONSFUNCTIONSMATHEMATICAL SOLUTIONSNONLINEAR PROBLEMSPARTIAL DIFFERENTIAL EQUATIONSQUASI PARTICLESSCHROEDINGER EQUATIONSOLITONSTHREE-DIMENSIONAL CALCULATIONSWAVE EQUATIONS

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Asad, R, Simpson, G. 2011-03-15. Embedded eigenvalues and the nonlinear Schroedinger equation. https://doi.org/10.1063/1.3567152

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