Rough solutions for the periodic Schrödinger--Korteweg--de Vries system
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Publication:855390
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
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
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- 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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