Zobrazeno 1 - 10
of 33
pro vyhledávání: '"Lech Zielinski"'
Autor:
Mirna Charif, Lech Zielinski
Publikováno v:
Opuscula Mathematica, Vol 41, Iss 3, Pp 301-333 (2021)
We investigate eigenvalue perturbations for a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. In particular we obtain explicit estimates for the convergence radius of the perturbation serie
Externí odkaz:
https://doaj.org/article/0836d49c859e4e76a0d1219e65a30f68
Publikováno v:
Opuscula Mathematica, Vol 40, Iss 2, Pp 241-270 (2020)
We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.
Externí odkaz:
https://doaj.org/article/274e383548b34b3691cd97d0fa1239ad
Autor:
Dmitry Shepelsky, Lech Zielinski
Publikováno v:
Opuscula Mathematica, Vol 37, Iss 1, Pp 167-187 (2017)
The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) is treated by the Riemann-Hilbert approach
Externí odkaz:
https://doaj.org/article/d97072a153d14de892e93f16e972569b
Autor:
Dmitry Shepelsky, Lech Zielinski
Publikováno v:
Opuscula Mathematica, Vol 37, Iss 1, Pp 167-187 (2017)
The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) is treated by the Riemann-Hilbert approach
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1546fbe77d38cfefa9c4f0335a9ba5ae
https://hal.archives-ouvertes.fr/hal-03663131
https://hal.archives-ouvertes.fr/hal-03663131
We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrodinger equation in the quarter plane x>0, t >0 in the case of periodic initial data, u(x,0) = α exp(−2iβx) (or asymptotically periodic, u(x, 0) =α exp(−2iβx)
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d03ab00f149da82a7fc98808e940db17
https://hal.archives-ouvertes.fr/hal-03662504
https://hal.archives-ouvertes.fr/hal-03662504
Autor:
Lech Zielinski, Anne Boutet de Monvel
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783030684891
We investigate the asymptotic behavior of large eigenvalue for the two-photon Rabi Hamiltonian, i.e., for the two-photon Jaynes–Cummings model without the rotating wave approximation. We prove that the spectrum of this Hamiltonian consists of two e
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::626044b743934b4349a21b6b1d2d3d57
https://doi.org/10.1007/978-3-030-68490-7_5
https://doi.org/10.1007/978-3-030-68490-7_5
Autor:
Lech Zielinski, Anne Boutet de Monvel
Publikováno v:
Analysis as a Tool in Mathematical Physics ISBN: 9783030315306
We investigate the behavior of large eigenvalues for the quantum Rabi Hamiltonian, i.e., for the Jaynes–Cummings model without the rotating wave approximation. The three-term asymptotics we obtain involves all the parameters of the model so that we
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bf8eb0f29a5e26c3b94e8987cd235afc
https://doi.org/10.1007/978-3-030-31531-3_13
https://doi.org/10.1007/978-3-030-31531-3_13
Publikováno v:
Letters in Mathematical Physics. 107:1345-1373
We develop a Riemann–Hilbert approach to the inverse scattering transform method for the short pulse (SP) equation $$\begin{aligned} u_{xt}=u+\tfrac{1}{6}(u^3)_{xx} \end{aligned}$$ with zero boundary conditions (as $$|x|\rightarrow \infty $$ ). Thi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::115d513e80d5bbbd5bfb37464368c1d1
https://doi.org/10.1007/s11005-017-0945-z
https://doi.org/10.1007/s11005-017-0945-z
Autor:
Lech Zielinski, Anne Boutet de Monvel
Publikováno v:
Journal of Spectral Theory. 7:559-631
We consider a class of unbounded self-adjoint operators including the Hamiltonian of the Jaynes-Cummings model without the rotating-wave approximation (RWA). The corresponding operators are defined by infinite Jacobi matrices with discrete spectrum.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2f71823cb3d9a7b333c1d4a127bdbe5c
https://doi.org/10.4171/jst/172
https://doi.org/10.4171/jst/172
Autor:
Lech Zielinski, Anne Boutet de Monvel
Publikováno v:
International Mathematics Research Notices
International Mathematics Research Notices, Oxford University Press (OUP), 2021, 2021 (7), pp.5155-5213. ⟨10.1093/imrn/rny294⟩
International Mathematics Research Notices, Oxford University Press (OUP), 2021, 2021 (7), pp.5155-5213. ⟨10.1093/imrn/rny294⟩
We investigate the large $n$ asymptotics of the $n$-th eigenvalue for a class of unbounded self-adjoint operators defined by infinite Jacobi matrices with discrete spectrum. In the case of the quantum Rabi model we obtain the first three terms of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6c705aad66d32a720ca8e601879c7588