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On Whitham's conjec...
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
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- Ehrnström, Mats (författare)
- Norwegian University of Science and Technology
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- Wahlén, Erik (författare)
- Lund University,Lunds universitet,Partiella differentialekvationer,Forskargrupper vid Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Partial differential equations,Lund University Research Groups,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- European Mathematical Society - EMS - Publishing House GmbH, 2019
- 2019
- Engelska.
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Ingår i: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. - : European Mathematical Society - EMS - Publishing House GmbH. - 0294-1449 .- 1873-1430. ; 36:6, s. 1603-1637
- Relaterad länk:
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http://dx.doi.org/10...
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http://arxiv.org/pdf...
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Abstract
Ämnesord
Stäng
- We consider the Whitham equation u t +2uu x +Lu x =0, where L is the nonlocal Fourier multiplier operator given by the symbol m(ξ)=tanhξ/ξ. G. B. Whitham conjectured that for this equation there would be a highest, cusped, travelling-wave solution. We find this wave as a limiting case at the end of the main bifurcation curve of P-periodic solutions, and give several qualitative properties of it, including its optimal C 1/2 -regularity. An essential part of the proof consists in an analysis of the integral kernel corresponding to the symbol m(ξ), and a following study of the highest wave. In particular, we show that the integral kernel corresponding to the symbol m(ξ) is completely monotone, and provide an explicit representation formula for it. Our methods may be generalised.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Full-dispersion models
- Global bifurcation
- Highest waves
- Whitham equation
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- ref (ämneskategori)
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