Db. Fairlie et An. Leznov, INFINITE SERIES SOLUTIONS OF THE SYMMETRY EQUATION FOR THE 1+2 DIMENSIONAL CONTINUOUS TODA CHAIN, Physics letters. A, 221(5), 1996, pp. 306-310
A sequence of solutions to the equation of symmetry for the continuous
Toda chain in 1 + 2 dimensions is represented in explicit form. This
fact leads to the supposition that this equation is completely integra
ble.