Variable separation and algebraic-geometric solutions of modified Toda lattice equation

摘要

In this paper, we derive a modified Toda lattice hierarchy by resorting to the Lenard operator pairs. The hyper-elliptic curve and AbelJacobi coordinates are then introduced to linearize the associated flow, from which some algebraic-geometric solutions of the modified Toda lattice are explicitly constructed in terms of Riemann theta functions by using Jacobi inversion technique.