
VOLUME 30  ISSUE 7 
PAGE 414

Integrability of the twodimensional generalization of Toda chain
Mikhailov A.V.
It is shown that a twodimensional generalization of the Toda chain φ ^{k}_{tt} —Æ^{Ë}_{ÈÈ }2 exp(2^ ^{k} ^{+}^{1} 2Æ^{Ë})+2 ÅÈÒ(2Æ ^{k} — 2Æ^{Ë}~^{1}) — 0 and, in particular, the equation Æ_{Ð} — Æ_{ÈÈ} f 2 exp(4 φ ) — 2 exp( — 2φ ) = 0 are integrable by the inverseproblem method. A group, which is noncommutative in the second case, reduces these equations.

Permission given by American Institute of Physics is appreciated.
