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Article Dans Une Revue Analysis & PDE Année : 2013

Stability and instability for subsonic travelling waves of the Nonlinear Schrö̈dinger Equation in dimension one

David Chiron

Résumé

We study the stability/instability of the subsonic travelling waves of the Nonlinear Schrödinger Equation in dimension one. Our aim is to propose several methods for showing instability (use of the Grillakis-Shatah-Strauss theory, proof of existence of an unstable eigenvalue via an Evans function) or stability. For the later, we show how to construct in a systematic way a Liapounov functional for which the travelling wave is a local minimizer. These approaches allow to give a complete stability/instability analysis in the energy space including the critical case of the kink solution. We also treat the case of a cusp in the energy-momentum diagram.
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Dates et versions

hal-00874585 , version 1 (18-10-2013)

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  • HAL Id : hal-00874585 , version 1

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David Chiron. Stability and instability for subsonic travelling waves of the Nonlinear Schrö̈dinger Equation in dimension one. Analysis & PDE, 2013, 6 (6), pp.1327-1420. ⟨hal-00874585⟩
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