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Differential-difference evolution equations. II (Darboux transformation for the Toda lattice)

✍ Scribed by V. B. Matveev; M. A. Salle

Publisher
Springer
Year
1979
Tongue
English
Weight
193 KB
Volume
3
Category
Article
ISSN
0377-9017

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✦ Synopsis

Toda lattice equation is represented in the form of the condition of compatibility of the system of linear equations corresponding to a non-Hermitian Lax representation. The Darboux invariance of this linear system is defined and proved in the text, and enables us to construct some new formulas for the solutions of the Toda lattice equation. These formulas involving determinants are applicable to an arbitrary initial solution of the Toda equation for example to a solution growing at infinity.

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