Seminar talk, 10 February 2010

Speaker: Joseph Krasil'shchik

Title: On integrable structures on the Hirota equation

Abstract:
The Hirota equation is obtained by covering the KdV one using the differential substitution $v=-2(\ln u)_{xx}$. This is a fourth-order non-evolution equation of a rather complicated form, (see the ref.). I shall describe how quite simple computations lead to description of Hamiltonian, simplectic, and recursion operators for this equation.

This is a join work with Paul Kersten and Alexander Verbovetsky.

References:
Hirota R. Exact solution of the Korteweg—de Vries equation for multiple collisions of solitons, Phys. Rev. Lett. 27 (1971), 1192-1194, doi:10.1103/PhysRevLett.27.1192