Jahresber. Deutsch. Math.-Verein. 103, no. 4, 149-162 (2001) [url]
Almost Everything You Always Wanted to Know About the Toda Equation
Gerald Teschl and Wien
The present article reviews methods from spectral theory and algebraic geometry for finding explicit solutions of the Toda equation, namely for the N-soliton solution and quasi-periodic solutions. Along they way basic concepts like Lax pairs, associated hierarchies, and Bäcklund transformations for the Toda equation are introduced.
Keywords: Toda equation, Kac van Moerbeke equation, Solitons, Lax pair}