Vsevolod Adler (Moscow) Title: Stationary solutions of non-autonomous symmetries of integrable equations
From OLLIE Quinn
Vsevolod Adler (Moscow)
Title: Stationary solutions of non-autonomous symmetries of integrable equations
The talk is about some recent results on Painleve-type reductions for integrable equations. My first example is a reduction obtained as a stationary equation for master-symmetry of KdV equation. It is equivalent to some fourth order ODE and numerical experiments show that some of its special solutions may be related to the Gurevich-Pitaevskii problem on decay of initial discontinuity. The second example is about non-Abelian Volterra lattices. Here we study several low-order reductions and demonstrate their relation with non-Abelian analogues of discrete and continuous Painleve equations.