Rough solutions for the periodic Schrödinger--Korteweg--de Vries system

DOI10.1016/J.JDE.2006.04.012zbMath1105.35087arXivmath/0511491OpenAlexW2222862121MaRDI QIDQ855390

Alexander Arbieto, Carlos Matheus, Adán J. Corcho

Publication date: 7 December 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511491

zbMATH Keywords

wave equationnonlinear Schrödinger equationKdV equationwave interactionwell-posed

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (5)

Internal null controllability of a linear Schrödinger-KdV system on a bounded interval ⋮ Control results for a model of resonant interaction between short and long capillary-gravity waves ⋮ The Cauchy problem for the Schrödinger-KdV system ⋮ Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger-Korteweg-de Vries interactions on the half-line ⋮ Recurrent solutions of the Schrödinger-KdV system with boundary forces

Cites Work

• Unnamed Item
• The Cauchy problem for a Schrödinger-Korteweg-de Vries system with rough data.
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• Interaction equations for short and long dispersive waves
• On the Cauchy problem for the Zakharov system
• Well-posedness for the Schrödinger-Korteweg-de Vries system
• A General Theory for Interactions Between Short and Long Waves
• Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation

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