Seminar talk, 8 December 2010

Speaker: Valentina Golovko

Title: Integrability and Hamiltonian formalism in $2+1$ dimensions

Abstract:
The talk will discuss the construction of recursion operators and Hamiltonian formalism in $2+1$ dimensions by examples of KP and DS (Davey-Stewartson) equations, $(2+1)$-AKNS hierarchy, as well as the classification of scalar evolutionary integrable equations in $2+1$ dimensions.

References:
Athorne C. and Dorfman I.Ya. The Hamiltonian structure of the $(2+1)$-dimensional Ablowitz-Kaup-Newell-Segur hierarchy, J. Math. Phys. 34 (1993) 3507-3517, doi:10.1063/1.530040

Fokas A.S. and Santini P.M. Recursion operators and bi-Hamiltonian structures in multidimensions. I, Commun. Math. Phys. 115 (1988) 375-419, doi:10.1007/BF01218017, http://projecteuclid.org/euclid.cmp/1104160997

Fokas A.S. and Santini P.M. Recursion operators and bi-Hamiltonian structures in multidimensions. II, Commun. Math. Phys. 116 (1988) 449-474, http://dx.doi.org/10.1007/BF01229203, http://projecteuclid.org/euclid.cmp/1104161422

Novikov V.S. and Ferapontov E.V. On the classification of scalar evolutionary integrable equations in $2+1$ dimensions, arXiv:1011.2145