Exact Results in Quantum Theory & Gravity

Ścisłe rezultaty teorii kwantów i grawitacji


prof. 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

Friday, 11.06.2021

Rostyslav Hryniv (Ukrainian Catholic University)

will give an on-line talk
joint with UJ and UAM

Generalized soliton solutions on the Korteweg-de Vries equation

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
16.10.2020 Jerzy Lewandowski (IFT) Penrose's spacetime singularity theorems winning the Nobel Prize
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
06.11.2020 Avery Ching (Hong Kong University of Science and Technology) The geometry of Rodrigues' formulae
13.11.2020 Maciej Lisicki (IFT) Pumping and swimming: two faces of phoretic flows
20.11.2020 Carlos Tamarit (Technical University of Munich) The strong CP problem, the infinite volume limit, and cluster decomposition
27.11.2020 Paweł Caputa (IFT) Exactly solvable deformations in Quantum Theory & Gravity
11.12.2020 Chiu-Yin Tsang (University of Hong Kong, Math. Dept.) Formal hypergeometric function series with I-adic topology
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)
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)

Schedules of previous academic years