The Darboux-like transform and some integrable cases of the q-Riccati equation

Journal of Physics A: Mathematical and General

Volumn 35, Issue 3, 2002, Pages 747-757

  Odzijewicz, Anatol ^a   Ryzko, Alina ^a  

^a UNIVERSITY OF BIALYSTOK   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037169452     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/3/318     Document Type: Article

References (15)

1. [C] Crum M M 1955 Associated Sturm-Liouville systems Q. J. Math. 6 121
2. [D] Darboux G 1882 C. R. Acad. Sci., Paris 94 1456
3. [I-H] Infeld L and Hull T E 1951 The factorization method Rev. Mod. Phys. 23 21
4. [L-R] De Lange O L and Raab R E 1991 Operator Methods in Quantum Mechanics (Oxford: Clarendon)
5. [M] Matveev V B 1992 Generalized Wronskian formula for solutions of the KdV equations: first applications Phys. Lett. A 166 205
6. [Ma] Matveev V B 1992 Positon-positon and soliton-positon collisions: KdV case Phys. Lett. A 166 209
7. [M-S] Matveev V B and Salle M A 1991 Darboux Transformations and Solitons (Berlin: Springer)
8. [Mi] Mielnik B, Nieto L M and Rosas-Ortiz O 2000 The finite difference algorithm for higher order supersymmetry Phys. Lett. A 269 70
9. [Mil] Miller W Jr 1968 Lie Theory and Special Functions (New York: Academic)
10. [N-D] Novikov S P and Dynnikov I A 1997 Discrete spectral symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds Russ. Math. Surv. 52 1057
11. [O] Odzijewicz A 1998 Quantum algebras and q-special functions related to coherent states maps of the disc Commun. Math. Phys. 192 183
12. [Ry-G] Ryżyk I M and Gradsztejn I C 1951 The Tables of Integrals, Sums, Series and Products (Moscow: GITTL) (in Russian)
13. [St] Stahlhofen A A 1992 Positons of the modified Korteweg de Vries equation Ann. Phys. 1 554
14. [Sta] Stahlhofen A A 1995 Completely transparent potentials for the Schrödinger equation Phys. Rev. A 51 934
15. [Su] Sujetin I K 1979 Classical Orthogonal Polynomials (Moscow: Nauka) (in Russian)