Integration of partially
integrable evolution equations
Professor
Robert Conte
CEA-Saclay, France
Abstract
In physics or fluid mechanics,
most evolution equations or wave equations are only partially integrable, and our problem is to explicitly integrate in
all particular cases where this is possible.
There exist several
suitable methods of complex analysis, but none is optimal. The theory of Nevanlinna and Wiman-Valiron on
the growth of the meromorphic solutions gives
predictions and bounds, but it is not constructive and restricted to meromorphic solutions. The Painlevé
approach via the a priori
singularities of the solutions gives no bounds but it is often (not always)
constructive. It seems that an adequate combination of the two methods could
yield much more output in terms of explicit (i.e. closed form) analytic
solutions. We will review this question, mainly taking the apparently simple
equation of Kuramoto and Sivashinsky
with constants. This
is a joint work with M. Musette and Yee Tat-leung.
Date: |
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Place: |
Room 517, Meng Wah Complex |
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All are welcome |
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