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Article Dans Une Revue Journal of Differential Equations Année : 2015

Orbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves

Résumé

Periodic waves of the one-dimensional cubic defocusing NLS equation are considered. Using tools from integrability theory, these waves have been shown in [4] to be linearly stable and the Floquet–Bloch spectrum of the linearized operator has been explicitly computed. We combine here the first four conserved quantities of the NLS equation to give a direct proof that cnoidal periodic waves are orbitally stable with respect to subharmonic perturbations, with period equal to an integer multiple of the period of the wave. Our result is not restricted to the periodic waves of small amplitudes.
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Dates et versions

hal-01227512 , version 1 (11-11-2015)

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Thierry Gallay, Dmitry Pelinovsky. Orbital stability in the cubic defocusing NLS equation: I. Cnoidal periodic waves. Journal of Differential Equations, 2015, 258 (10), pp.3607-3638. ⟨10.1016/j.jde.2015.01.018⟩. ⟨hal-01227512⟩
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