Solution of infinite Toda chains (Q1178116)

Considering the infinite system of ordinary differential equations \(da_ n/dt=1/2a_ n(b_{n+1}-b_ n)\), \(db_ n/dt=a_ n^ 2-a^ 2_{n- 1}\), \(n\in Z\), with bounded initial data \(| a_ n(0)|\leq c\), \(| b_ n(0)|\leq c\), the author proves solvability and the uniqueness of solution to an initial value problem on \([0,\delta(c)]\). Besides, he establishes that this solution can be expanded into a series in powers of \(t\) and defines the coefficients of the expansion.