Global Well-Posedness and Long-time Asymptotics for the Defocussing Davey-Stewartson II Equation in $H^{1,1}(R^2)$

Abstract

We show that the inverse scattering map for the linear system associated with the defocussing Davey-Stewartson II equation is locally Lipschitz continuous with locally Lipschitz continuous inverse on $H^{1,1}(R^2)$. From the inverse scattering method we then obtain global well-posedness for the defocussing Davey-Stewartson II equation. We show that these global solutions are dispersive by computing their leading asymptotic behavior as $t\to \infty$ in terms of an associated linear problem.

42 pages. Revised and corrected according to referee comments. To appear in J. Spectral Theory

References in corpus (3)

• Miura Maps and Inverse Scattering for the Novikov-Veselov Equation
• The Novikov-Veselov Equation and the Inverse Scattering Method, Part I: Analysis
• Estimates for a family of multi-linear forms

Cited by in corpus (3)

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• A numerical approach to Blow-up issues for Davey-Stewartson II type systems
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