On the Fay identity for Korteweg-de Vries tau functions and the identity for the Wronskian of squared solutions of Sturm-Liouville equation. (English) Zbl 0952.37032
The author demonstrates that the famous identity for the Wronskian of squared solutions of the Sturm-Liouville equation follows from the Fay identity for KdV tau functions. Some specific relations for the KdV tau function are obtained.
Reviewer: Samir Musayev (Baku)
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 14H42 | Theta functions and curves; Schottky problem |
| 14H70 | Relationships between algebraic curves and integrable systems |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
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