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Zbl 1039.37058
Teschl, Gerald
Almost everything you always wanted to know about the Toda equation. (English)
[J] Jahresber. Dtsch. Math.-Ver. 103, No. 4, 149-162 (2001). ISSN 0012-0456

From the text: 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. The contents constitute an extended version of my talk given at the joint annual meeting of the Österreichische Mathematische Gesellschaft und der Deutsche Mathematiker-Vereinigung in September 2001, Vienna, Austria.

MSC 2000:: *37K10 Completely integrable systems etc.
37K40 Soliton theory, asymptotic behavior of solutions
37K60 Lattice dynamics

Keywords: $N$-soliton solution; quasi-periodic solutions; Lax pairs; hierarchies; Bäcklund transformations

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