Events Calendar
Oct 30
14:00 - 15:00
Mathematical Physics & Integrable Systems seminar: Alexander Mikhailov (University of Leeds)
SMSAS Mathematical Physics seminars
Polynomial integrable Hamiltonian systems on symmetric powers of plain curves

We have found k integrable Hamiltonian systems on C^{2k} (or on R^{2k}, if the base field is R), naturally defined by a symmetric power Sym^k (V_g) of a plain algebraic curve V_g of genus g. When k=g the symmetric power Sym^k (V_g) is bi-rationally isomorphic to the Jacobian of the curve V_g and our system is equivalent to the well known Dubrovin's system which has been derived and studied in the theory of finite gap solutions (algebra-geometric integration) of the Korteweg-de Vries equation. We have found the coordinates in which the systems obtained and their Hamiltonians are polynomial. For k=2, g=1,2,3 we present these systems explicitly as well as we discuss the problem of their integration. In particular, if k=2, g>2 the solution of the systems is not a 2g periodic Abelian function.


Sibson Building (SibSR2)
United Kingdom


Open to All interested persons,

Contact: Dr Pavlos Xenitidis
School of Mathematics, Statistics and Actuarial Science


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Last Updated: 10/01/2012