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Non-linear wave and Schrödinger equations

I. Instability of periodic and quasiperiodic solutions

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Abstract

We investigate stability of periodic and quasiperiodic solutions of linear wave and Schrödinger equations under non-linear perturbations. We show in the case of the wave equations that such solutions are unstable for generic perturbations. For the Schrödinger equations periodic solutions are stable while the quasiperiodic ones are not. We extend these results to periodic solutions of non-linear equations.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Ontario, Canada

    I. M. Sigal (I.W. Killiam Research Fellow)

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  1. I. M. Sigal
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Communicated by T. Spencer

Partially supported by NSERC under Grant NA7901

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Sigal, I.M. Non-linear wave and Schrödinger equations. Commun.Math. Phys. 153, 297–320 (1993). https://doi.org/10.1007/BF02096645

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  • DOI: https://doi.org/10.1007/BF02096645

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