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 |
References:
[1] | DOI: 10.1007/BF02099527 · Zbl 0756.35074 · doi:10.1007/BF02099527 |
[2] | DOI: 10.1007/BF01388967 · Zbl 0621.35097 · doi:10.1007/BF01388967 |
[3] | DOI: 10.1088/0266-5611/7/3/006 · Zbl 0738.34045 · doi:10.1088/0266-5611/7/3/006 |
[4] | Wilson G., C. R. Acad. Sci., Ser. I: Math. 299 (13) pp 587– (1984) |
[5] | DOI: 10.1006/aima.1994.1070 · Zbl 0814.35114 · doi:10.1006/aima.1994.1070 |
[6] | DOI: 10.1007/BF02103276 · Zbl 0811.35105 · doi:10.1007/BF02103276 |
[7] | DOI: 10.1080/00036819708840565 · Zbl 0937.30025 · doi:10.1080/00036819708840565 |
[8] | DOI: 10.1080/00036819708840541 · Zbl 0887.14011 · doi:10.1080/00036819708840541 |
[9] | Mishev Y. P., Matematica Balkanika 11 (1) pp 139– (1997) |
[10] | Mishev Y. P., Matematica Balkanika 11 (3) pp 275– (1997) |
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