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Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation

Abstract:

The formation of shocks in waves of advance in nonlinear partial differential equations is a well-explored problem and has been studied using many different techniques. In this paper we demonstrate how an exponential-asymptotic approach can be used to completely characterize the shock formation in a nonlinear partial differential equation and so resolve an apparent paradox concerning the asymptotic modelling of shock formation. In so doing, we find that the recently discovered higher-order St...

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Publication status:
Published

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Publisher copy:
10.1088/0951-7715/20/10/009

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Olde Daalhuis, AB More by this author
Journal:
NONLINEARITY
Volume:
20
Issue:
10
Pages:
2425-2452
Publication date:
2007-10-05
DOI:
EISSN:
1361-6544
ISSN:
0951-7715
URN:
uuid:ffec0be3-9d56-4f43-b814-035e86e5680e
Source identifiers:
25800
Local pid:
pubs:25800
Language:
English

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