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Quantisation of Kadomtsev-Petviashvili equation

Presented by: 
Evgeny Sklyanin
Thursday 14th January 2016 - 16:30 to 17:30
INI Seminar Room 1
Co-authors: Karol Kozlowski (Institut de mathematiques de Bourgogne, Dijon, France), Alessandro Torrielli (University of Surrey)

A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of one-dimensional bosons carrying masses m=1,2,... The Hamiltonian is Galilei-invariant and includes the cubic split/merge (m1,m2)(m1+m2) terms for all combinations of particles with masses m1, m2 and m1+m2, with a special choice of coupling constants. The Bethe eigenfunctions for the model are constructed. The consistency of the coordinate Bethe ansatz, and therefore, the quantum integrability of the model is verified for the sectors up to the total mass M=8. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons