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A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations
journal contribution
posted on 2018-10-04, 10:46 authored by Jonathan EckhardtJonathan Eckhardt, Gerald TeschlWe propose a novel technique for analysing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has a purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for
the usual Riemann–Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa–Holm equation.
Funding
Research supported by the Austrian Science Fund (FWF) under Grant No. Y330 and by the AXA Research Fund under the Mittag-Leffler Fellowship Project.
History
School
- Science
Department
- Mathematical Sciences
Published in
NonlinearityVolume
29Issue
3Pages
1036 - 1046Citation
ECKHARDT, J. and TESCHL. G., 2016. A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations. Nonlinearity, 29(3), pp. 1036 - 1046Publisher
© IOP Publishing Ltd & London Mathematical SocietyVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution 3.0 Unported (CC BY 3.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/Publication date
2016-02-04Notes
This is an Open Access Article. It is published by IOP under the Creative Commons Attribution 3.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/ISSN
0951-7715eISSN
1361-6544Publisher version
Language
- en