On the spectral curve for functional-difference Schrödinger equation
Article
First Online:
Received:
We suggest a method for constructing a set of finite-gap solutions for a functional-difference deformation of the Schrödinger equation v(x)f(x +2h)+ f(x)= λf(x + h). It is shown that the edges of gaps of the corresponding spectral curve depend on x. Examples are given. Bibliography: 7 titles.
Keywords
Russia Order Equation Spectral Curve Casorati Determinant Aerospace Instrument
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.J. F. van Diejen, “Integrability of difference Calogero-Moser systems,” J. Math. Phys., 35, 2983–3004 (1994).MATHCrossRefMathSciNetGoogle Scholar
- 2.P. Gaillard, “A new family of deformations of Darboux-Pöshl-Teller potentials,” Lett. Math. Phys., 68, 77–90 (2004).MATHCrossRefMathSciNetGoogle Scholar
- 3.V. B. Matveev, “Functional-difference deformations of Darboux-Pöshl-Teller potentials,” in: L. Faddeev, P. van Moerbeke, and F. Lambert (eds.), Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete, NATO Science Series, Springer (2006), pp. 191–2008.Google Scholar
- 4.P. Gailard and V. B. Matveev, “New formulas for the eigenfuntions of the two-particle difference Calogero-Moser system,” preprint (2009), pp. 1–15.Google Scholar
- 5.I. M. Krichever, “Algebraic curves and nonlinear difference equations,” Usp. Mat. Nauk, 33, 215–216 (1978).MATHMathSciNetGoogle Scholar
- 6.A. O. Smirnov, “Elliptic solitons and Heun equation,” CRM Proc. Lect. Notes., 32, 287–305 (2002).Google Scholar
- 7.A. O. Smirnov, “Finite-gap solutions of the Fuchsian equation,” Lett. Math. Phys., 76, 297–316 (2006).MATHCrossRefMathSciNetGoogle Scholar
Copyright information
© Springer Science+Business Media, Inc. 2010