Exact Results in Quantum Theory & GravityŚcisłe rezultaty teorii kwantów i grawitacji2019/2020prof. dr hab. Jan Dereziński, prof. dr hab. Krzysztof Meissner dr Wojciech Kamiński, dr Grzegorz Łach Pasteura 5, room 1.40, Fridays 14:15 - < 16:00 |
The Korteweg--de Vries (KdV) equation is a non-linear dispersive equation describing
shallow-water waves and possessing many intriguing properties. One of them is existence of
the so-called soliton solutions representing solitary waves travelling with constant speed
and shape, as well as a special way in which several such solitons interact. Another
interesting fact is that solutions of the KdV can be obtained as solutions of the inverse
scattering problem for the family of associated Schroedinger operators, as discovered by
S.Gardner, J.Green, M.Kruskal and R.Miura in 1967, and the classical soliton solutions of the
KdV correspond precisely to the so-called reflectionless potentials (I.Kay and H.Moses,
1956).
The aim of this talk is two-fold. Firstly, we characterise the family of all Schroedinger
operators with integrable reflectionless potentials and give an explicit formula producing
all such potentials. Secondly, we use the inverse scattering transform approach to describe
all solutions of the KdV equation whose initial (t=0) profile is an integrable reflectionless
potential. Such solutions will stay integrable and reflectionless for all positive times and
can be called generalized soliton solutions of KdV. This research extends and specifies in
several ways the previous work on reflectionless potentials by V.Marchenko, C.Remling et al.
and generalized soliton solutions of the KdV equation introduced by V.Marchenko in 1991 and
F.Gesztesy, W.Karwowski, and Z.Zhao in 1992. The talk is based on a joint project with
B.Melnyk and Ya.Mykytyuk (Lviv Franko National University).
Date | Speaker | Title | Slides |
---|---|---|---|
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23.10.2020 | Marcin Napiórkowski (KMMF) | Optimal rate of condensation for trapped bosons in the Gross-Pitaevskii regime | |
30.10.2020 | Adam Bednorz (IFT) | Free will in quantum physics | Slides |
06.11.2020 | Avery Ching (Hong Kong University of Science and Technology) | The geometry of Rodrigues' formulae | Slides |
13.11.2020 | Maciej Lisicki (IFT) | Pumping and swimming: two faces of phoretic flows | Movie_1 |
20.11.2020 | Carlos Tamarit (Technical University of Munich) | The strong CP problem, the infinite volume limit, and cluster decomposition | Slides |
27.11.2020 | Paweł Caputa (IFT) | Exactly solvable deformations in Quantum Theory & Gravity | |
04.12.2020 | — | — | |
11.12.2020 | Chiu-Yin Tsang (University of Hong Kong, Math. Dept.) | Formal hypergeometric function series with I-adic topology | Slides |
18.12.2020 | Yik Man Chiang (Hong Kong University of Science and Technology) | Picard's theorems with respects to difference operators | |
15.01.2021 | Andrzej Herdegen (Jagiellonian University) | Infrared problem vs gauge choice: scattering of Dirac field | |
22.01.2021 | Yik Man Chiang (Hong Kong University of Science and Technology) | Resolving apparent singularities of Heun connections | |
29.01.2021 | Maciej Łebek (IFT/CFT) | Single- to many-body crossover of a quantum carpet | |
05.03.2021 | no seminar | ||
12.03.2021 | Abhishek Goswami (SUNY) | Mass gap in U(1) Higgs-Yukawa model on a unit lattice (joint seminar with UJ and UAM) | |
19.03.2021 | Paweł Duch (Universität Leipzig) | Renormalization of the stochastic quantization equation of the Phi^4_3 model with the use of the Polchinski flow
equation (joint seminar with UJ and UAM) | |
26.03.2021 | Oskar Grocholski (FUW) | Bessel operators as a toy model of Wilsonian renormalization | |
31.03.2021 | David Matejov | Uniqueness of extremal isolated horizons and their identification with horizons of all type D black holes | |
09.04.2021 | Michał Wrochna (Cergy Paris Université) | Spectral actions on asymptotically Minkowski spacetimes (joint seminar with UJ and UAM) | Slides |
16.04.2021 | Vitaly Moroz (Swansea University) | Thomas-Fermi type models for graphene (joint seminar with UJ and UAM) | |
23.04.2021 | Jan Chojnacki (FUW) | Cosmological predictions from infinite classical action | |
30.04.2021 | Léo Morin (ENS Rennes) | Spectral theory of the semiclassical magnetic Laplacian | |
14.05.2021 | Katarzyna Rejzner (University of York) | Equilibrium states for the massive Sine-Gordon theory
in the Lorentzian signature (joint seminar with UJ and UAM) | |
21.05.2021 | Itay Griniasty (Cornell University) | Generating multiple surfaces from a single inhomogeneous anisotropically deforming sheet | |
28.05.2021 | Joseph Viola (Université de Nantes) | The spectral decomposition and the Schrödinger evolution for non-self-adjoint degree-2
Hamiltonians
(joint seminar with UJ and UAM) | |
11.06.2021 | Rostyslav Hryniv (Ukrainian Catholic University) | Generalized soliton solutions on the Korteweg-de Vries
equation (joint seminar with UJ and UAM) |