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Article Dans Une Revue J. Hyperbolic Differ. Equ. Année : 2007

Cascade of phase shifts for nonlinear Schrödinger equations

Résumé

We consider a semi-classical nonlinear Schrödinger equation. For initial data causing focusing at one point in the linear case, we study a nonlinearity which is super-critical in terms of asymptotic effects near the caustic. We prove the existence of infinitely many phase shifts appearing at the approach of the critical time. This phenomenon is suggested by a formal computation. The rigorous proof shows a quantitatively different asymptotic behavior. We explain these aspects, and discuss some problems left open.

Dates et versions

hal-00004970 , version 1 (24-05-2005)

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Rémi Carles. Cascade of phase shifts for nonlinear Schrödinger equations. J. Hyperbolic Differ. Equ., 2007, 4 (2), pp.207-231. ⟨10.1142/S0219891607001112⟩. ⟨hal-00004970⟩
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