Higher Toda Mechanics and Spectral Curves

For each of the Lie algebras gln and gl～n., we construct a family of integrable generalizations of the Toda chains characterized by two integers m+ and m-. The Lax matrices and the equations of motion are given explicitly, and the integrals of motion can be calculated in terms of the trace of powers of the Lax matrix L. For the case of m+ = m-,we find a symmetric reduction for each generalized Toda chain we found, and the solution to the initial value problems of the reduced systems is outlined. We also studied the spectral curves of the periodic (m+,m-)-Toda chains, which turns out to be very different for different pairs of m+ and m-. Finally we also obtain thenonabelian generalizations of the (m+, m-)-Toda chains in an explicit form.

作 者： ZHAO Liu LIU Wang-Yun   作者單位： Institute of Modern Physics, Northwest University, Xi'an 710069, China  刊 名： 理論物理通訊(英文版)  ISTIC SCI 英文刊名： COMMUNICATIONS IN THEORETICAL PHYSICS  年，卷(期)： 2004 42(7)  分類號：   關(guān)鍵詞： Toda chain   Lax matrix   symmetric reduction   spectral curves  

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