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pro vyhledávání: '"Eckhardt, Jonathan"'
Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data
Autor:
Eckhardt, Jonathan
We show that solutions of the Korteweg-de Vries equation with reflectionless integrable initial data decompose into a (in general infinite) linear superposition of solitons after long enough time. The proof is based on a representation of reflectionl
Externí odkaz:
http://arxiv.org/abs/2311.01878
Autor:
Eckhardt, Jonathan, Kostenko, Aleksey
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szeg\H{o}-type theorems for generaliz
Externí odkaz:
http://arxiv.org/abs/2311.01189
Autor:
Eckhardt, Jonathan, Kostenko, Aleksey
We extend the inverse spectral transform for the conservative Camassa-Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness-type conditions at the other endpoint. The latter condition ap
Externí odkaz:
http://arxiv.org/abs/2310.06658
Autor:
Eckhardt, Jonathan, Kostenko, Aleksey
Publikováno v:
"From Complex Analysis to Operator Theory: A Panorama. In Memory of Sergey Naboko", M. Brown (ed.) et al., Oper. Theory Adv. Appl. 291, 435-474 (2023)
We establish criteria for the spectrum of a generalized indefinite string to be purely discrete and to satisfy Schatten-von Neumann properties. The results can be applied to the isospectral problem associated with the conservative Camassa-Holm flow a
Externí odkaz:
http://arxiv.org/abs/2106.13138
Autor:
Eckhardt, Jonathan
Publikováno v:
Bull. Lond. Math. Soc. 54 (2022), no. 2, 737-759
We employ some results about continued fraction expansions of Herglotz-Nevanlinna functions to characterize the spectral data of generalized indefinite strings of Stieltjes type. In particular, this solves the corresponding inverse spectral problem t
Externí odkaz:
http://arxiv.org/abs/2003.11653
Akademický článek
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Publikováno v:
J. Differential Equations 268 (2020), no. 6, 3016-3034
This article is concerned with the isospectral problem \[ -f'' + \frac{1}{4} f = z\omega f + z^2 \upsilon f \] for the periodic conservative Camassa-Holm flow, where $\omega$ is a periodic real distribution in $H^{-1}_{\mathrm{loc}}(\mathbb{R})$ and
Externí odkaz:
http://arxiv.org/abs/1907.01911
Publikováno v:
Israel J. Math. 250, 307-344 (2022)
We continue to investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two more model examples of generalized indefinit
Externí odkaz:
http://arxiv.org/abs/1906.05106
Autor:
Eckhardt, Jonathan, Kostenko, Aleksey
Publikováno v:
Ann. Henri Poincar\'e 22, no.11, 3529-3564 (2021)
We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite strings under r
Externí odkaz:
http://arxiv.org/abs/1902.07898
Autor:
Eckhardt, Jonathan, Kostenko, Aleksey
Publikováno v:
Int. Math. Res. Notices (IMRN), vol. 2020, no. 16, 5126-5151 (2020)
We solve the inverse spectral problem associated with periodic conservative multi-peakon solutions of the Camassa-Holm equation. The corresponding isospectral sets can be identified with finite dimensional tori.
Comment: 18 pages, 1 figure
Comment: 18 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/1801.04612