Qualitative Features of Periodic Solutions of KdV

DOI10.1080/03605302.2013.814141zbMath1274.35330arXiv1110.0455OpenAlexW2034616400MaRDI QIDQ2855224

Beat Schaad, Peter J. Topalov, Thomas Kappeler

Publication date: 24 October 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.0455

zbMATH Keywords

smoothing propertiesKdV equationBirkhoff coordinatesAiry equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (16)

Regularity properties of the cubic nonlinear Schrödinger equation on the half line ⋮ Normal form coordinates for the Benjamin-Ono equation having expansions in terms of pseudo-differential operators ⋮ Smoothing and growth bound of periodic generalized Korteweg–De Vries equation ⋮ Tame majorant analyticity for the Birkhoff map of the defocusing nonlinear Schrödinger equation on the circle ⋮ Large KAM tori for quasi-linear perturbations of KdV ⋮ On the wellposedness of the KdV/KdV2 equations and their frequency maps ⋮ Birkhoff coordinates for the Toda lattice in the limit of infinitely many particles with an application to FPU ⋮ On the wellposedness of the KdV equation on the space of pseudomeasures ⋮ Normal form coordinates for the KdV equation having expansions in terms of pseudodifferential operators ⋮ Asymptotics of spectral quantities of Zakharov-Shabat operators ⋮ Qualitative Features of Periodic Solutions of KdV ⋮ On nonlinear interpolation ⋮ Dynamics of periodic Toda chains with a large number of particles ⋮ On longtime dynamics of perturbed KdV equations ⋮ Results on qualitative features of periodic solutions of KdV ⋮ One smoothing property of the scattering map of the KdV on \(\mathbb{R}\)

Cites Work

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