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VOLUME 30 (1979) | ISSUE 7 | PAGE 443
Integrability of the two-dimensional generalization of Toda chain
It is shown that a two-dimensional generalization of the Toda chain φ ktt —ÆËÈÈ 2 exp(2^ k +1 -2ÆË)+2 ÅÈÒ(2Æ k — 2ÆË~1) — 0 and, in particular, the equation ÆÐ — ÆÈÈ -f 2 exp(4 φ ) — 2 exp( — 2φ ) = 0 are integrable by the inverse-problem method. A group, which is noncommutative in the second case, reduces these equations.