Global well-posedness and scattering for the Dysthe equation in \(L^2(\mathbb{R}^2)\)
DOI10.1016/j.matpur.2020.11.001zbMath1467.35261arXiv2007.01613OpenAlexW3095052573MaRDI QIDQ2661961
Didier Pilod, Jean Claude Saut, Răzvan O. Moşincat
Publication date: 8 April 2021
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2007.01613
PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
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Cites Work
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- Well-posedness and ill-posedness results for the Novikov-Veselov equation
- The Fourier restriction norm method for the Zakharov-Kuznetsov equation
- A note on the Cauchy problem for the 2D generalized Zakharov-Kuznetsov equations
- Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth
- Well-posedness for a higher-order Benjamin-Ono equation
- Global well-posedness for the KP-II equation on the background of a non-localized solution
- A Hamiltonian approach to nonlinear modulation of surface water waves
- Analytic solutions to nonelliptic nonlinear Schrödinger equations
- Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation
- Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]
- Note on the modified nonlinear Schrödinger equation for deep water waves
- A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water
- Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study
- Hamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep water
- Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications
- Restriction for homogeneous polynomial surfaces in $\mathbb {R}^3$
- Hamiltonian form of the modified nonlinear Schrödinger equation for gravity waves on arbitrary depth
- On modifications of the Zakharov equation for surface gravity waves
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- On weakly nonlinear modulation of waves on deep water
- Well-Posedness for the Two-Dimensional Modified Zakharov–Kuznetsov Equation
- Local Smoothing and Local Solvability for Third Order Dispersive Equations
- On a fourth-order envelope equation for deep-water waves
- The fourth-order evolution equation for deep-water gravity-capillary waves
- A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation
- Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
- The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics
- The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves
- Frequency downshift in three-dimensional wave trains in a deep basin
- Dispersion Estimates for Third Order Equations in Two Dimensions
- Dispersive estimates for principally normal pseudodifferential operators
- A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
- Observations on the evolution of wave modulation
- Unsteady water wave modulations: Fully nonlinear solutions and comparison with the nonlinear Schrödinger equation.
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