The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: as the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vector are a novel and effective paradigm for describing extreme nonlinear phenomena.
%0 Journal Article
%1 2016arXiv160105796C
%A Braidotti, Maria Chiara
%A Gentilini, Silvia
%A Conti, Claudio
%D 2016
%J Optics Express
%K myown
%N 19
%P 21963
%T Gamow Vectors Explain the Shock ''Batman'' Profile
%U https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-19-21963&origin=search
%V 24
%X The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: as the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vector are a novel and effective paradigm for describing extreme nonlinear phenomena.
@article{2016arXiv160105796C,
abstract = {The description of shock waves beyond the shock point is a challenge in nonlinear physics. Finding solutions to the global dynamics of dispersive shock waves is not always possible due to the lack of integrability. Here we propose a new method based on the eigenstates (Gamow vectors) of a reversed harmonic oscillator in a rigged Hilbert space. These vectors allow analytical formulation for the development of undular bores of shock waves in a nonlinear nonlocal medium. Experiments by a photothermal induced nonlinearity confirm theoretical predictions: as the undulation period as a function of power and the characteristic quantized decays of Gamow vectors. Our results demonstrate that Gamow vector are a novel and effective paradigm for describing extreme nonlinear phenomena.},
added-at = {2016-08-17T08:10:16.000+0200},
adsnote = {Provided by the SAO/NASA Astrophysics Data System},
adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160105796C},
archiveprefix = {arXiv},
author = {Braidotti, Maria Chiara and Gentilini, Silvia and Conti, Claudio},
biburl = {https://www.bibsonomy.org/bibtex/208c4e9ddb70482a9d79fcb476f0c39bc/nonlinearxwaves},
eprint = {1601.05796},
interhash = {32d1dbf9bf06303ec8db37e57ea3b59c},
intrahash = {08c4e9ddb70482a9d79fcb476f0c39bc},
journal = {Optics Express},
keywords = {myown},
number = 19,
pages = 21963,
primaryclass = {nlin.PS},
timestamp = {2016-10-09T12:28:08.000+0200},
title = {Gamow Vectors Explain the Shock ''Batman'' Profile},
url = {https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-19-21963&origin=search},
volume = 24,
year = 2016
}