Geometry Seminar


Integration of partially

integrable evolution equations


Professor Robert Conte

CEA-Saclay, France




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 image010 constants. This is a joint work with M. Musette and Yee Tat-leung.




December 1, 2005 (Thursday)


4:00 – 5:00pm


Room 517, Meng Wah Complex




All are welcome