On positive type initial profiles for the KdV equation
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Publication:5418524
DOI10.1090/S0002-9939-2014-11943-5zbMath1294.35122arXiv1108.2314OpenAlexW1994531102MaRDI QIDQ5418524
Alexei Rybkin, Sergei M. Grudsky
Publication date: 4 June 2014
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1108.2314
well-posednessHankel operatormeromorphic functionspositonMiura transformTitchmarsh-Weyl functionsstep-like initial conditions
Related Items (9)
Trace formulas for additive and non-additive perturbations ⋮ Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm–Liouville operators ⋮ The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles ⋮ Global well-posedness for \(H^{-1}(\mathbb{R})\) perturbations of KdV with exotic spatial asymptotics ⋮ KdV equation beyond standard assumptions on initial data ⋮ Invertibility issues for Toeplitz plus Hankel operators and their close relatives ⋮ Soliton Theory and Hankel Operators ⋮ KdV on an incoming tide ⋮ Scattering theory for delta-type potentials
Cites Work
- Positons: Slowly decreasing analogues of solitons
- Introduction to the theory of Toeplitz operators with infinite index. Transl. from the Russian by Andrei Iacob
- The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step-like initial profile decaying on the right half line
- Meromorphic solutions to the KdV equation with non-decaying initial data supported on a left half line
- On the Cauchy problem for the Korteweg–de Vries equation with steplike finite-gap initial data: I. Schwartz-type perturbations
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- Toeplitz operators with frequency modulated semi-almost periodic symbols
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