A rather readable reference for this is [Deift, Li, Tomei, Toda flows with infinitely many variables, JFA 64 (1985), 358-402][1]Deift, Li, Tomei, Toda flows with infinitely many variables, JFA 64 (1985), 358-402 (who attribute the result to Moser). [1]: http://www.sciencedirect.com/science/article/pii/0022123685900655