Toda equation review

Teschl G.

The present article reviews methods from spectral theory and algebraic geometry for ending 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 Blacklund transformations for the Toda equation are introduced.

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Table of contents :
The Toda equation……Page 1
Complete integrability and Lax pairs……Page 4
Types of solutions……Page 5
The Toda hierarchy……Page 6
The Kac-van Moerbeke hierarchy……Page 7
Stationary solutions……Page 9
Jacobi operators associated with stationary solutions……Page 10
Algebro-geometric solutions of the Toda equations……Page 12