Darboux transformations for a system of coupled discrete Schrödinger equations

Physics of Atomic Nuclei

Volumn 65, Issue 8, 2002, Pages 1553-1559

  Suzko, A A ^a,b  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

^b JOINT INSTITUTE FOR POWER AND NUCLEAR RESEARCH SOSNY   (Belarus)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036695937     PISSN: 10637788     EISSN: None     Source Type: Journal    
DOI: 10.1134/1.1501668     Document Type: Article

References (39)

1. G. Darboux, C. R. Acad. Sci. 94, 1456 (1882).
2. E. Schrödinger, Proc. R. Ir. Acad. A, Math. Phys. Sci. 46, 9, 183 (1940).
3. L. Infeld and T. E. Hull, Rev. Mod. Phys. 23, 21 (1951).
4. E. Witten, Nucl. Phys. B 188, 513 (1981).
5. V. Bargmann, Phys. Rev. 75, 301 (1949); Rev. Mod. Phys. 21, 488 (1949).
6. V. Bargmann, Phys. Rev. 75, 301 (1949); Rev. Mod. Phys. 21, 488 (1949).
7. M. M. Nieto, Phys. Lett. B 145B, 208 (1984); C. V. Sukumar, J. Phys. A 18, 2937 (1985).
8. M. M. Nieto, Phys. Lett. B 145B, 208 (1984); C. V. Sukumar, J. Phys. A 18, 2937 (1985).
9. B. F. Samsonov, J. Phys. A 28, 6989 (1995); J. Math. Phys. (N.Y.) 39, 967 (1998).
10. B. F. Samsonov, J. Phys. A 28, 6989 (1995); J. Math. Phys. (N.Y.) 39, 967 (1998).
11. A. A. Suzko, Int. J. Mod. Phys. A 12, 277 (1997).
12. A. A. Suzko, Phys. Scr. 31, 447 (1985).
13. A. A. Suzko, Phys. Scr. 34, 5 (1986).
14. A. A. Suzko, Fiz. Élem. Chastits At. Yadra 24, 1133 (1993) [Phys. Part. Nucl. 24, 485 (1993)]; Lecture Notes in Physics, Ed. by H. von Geramb (Springer-Verlag, Berlin, 1993), Vol. 427, p. 67.
15. A. A. Suzko, Fiz. Élem. Chastits At. Yadra 24, 1133 (1993) [Phys. Part. Nucl. 24, 485 (1993)]; Lecture Notes in Physics, Ed. by H. von Geramb (Springer-Verlag, Berlin, 1993), Vol. 427, p. 67.
16. K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory (Springer-Verlag, Berlin, 1989, 2nd ed.; Mir, Moscow, 1980, translation of 1st ed.).
17. Lecture Notes in Physics (Springer-Verlag, Berlin, 1993), Vol. 427.
18. Lecture Notes in Physics (Springer-Verlag, Berlin, 1997), Vol. 488.
19. B. N. Zakhariev and A. A. Suzko, Direct and Inverse Problems. Potentials in Quantum Scattering (Springer-Verlag, Berlin, 1990).
20. S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: the Inverse Scattering Method (Nauka, Moscow, 1980; Consultants Bureau, New York, 1984).
21. F. Calogero and A. Degasperis, Spectral Transformation and Solitons (North-Holland, Amsterdam, 1982; Mir, Moscow, 1985).
22. V. B. Matveev and M. A. Salle, Darboux Transformations and Solitons (Springer-Verlag, Berlin, 1991), Springer Series in Nonlinear Dynamics.
23. V. B. Matveev and M. A. Salle, Lett. Math. Phys. 3, 425 (1979).
24. Z. S. Agranovich and V. A. Marehenko, Inversion Problem of Scattering Theory (Kharkov State Univ. Press, Kharkov, 1960; Gordon and Breach, New York, 1963).
25. M. Humi, J. Phys. A 18, 1085(1985).
26. A. A. Suz'ko, Yad. Fiz. 55, 2446 (1992) [Sov. J. Nucl. Phys. 55, 1359 (1992)].
27. J. M. Sparenberg and D. Baye, Phys. Rev. Lett. 79, 3802 (1997).
28. Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators (Naukova Dumka, Kiev, 1965; American Mathematical Society, Providence, 1968).
29. V. Spiridonov and A. Zhedanov, Methods Appl. Anal. 2, 369 (1995); J. Phys. A 30, 8727 (1997).
30. V. Spiridonov and A. Zhedanov, Methods Appl. Anal. 2, 369 (1995); J. Phys. A 30, 8727 (1997).
31. K. M. Case and M. Kac, J. Math. Phys. (N.Y.) 14, 594 (1973); K. M. Case, J. Math. Phys. (N.Y.) 15, 2166 (1974).
32. K. M. Case and M. Kac, J. Math. Phys. (N.Y.) 14, 594 (1973); K. M. Case, J. Math. Phys. (N.Y.) 15, 2166 (1974).
33. F. Gesztezy and B. Simon, in Proceedings of the International Conference "Mathematical Results in Quantum Mechanics," Prague, 1998.
34. T. S. Chihara, Introduction to Orthogonal Polynomials (Gordon and Breach, New York, 1978); G. Szegö, Orthogonal Polynomials (American Mathematical Society, New York, 1959, 4th ed.; Inostrannaya Literatura, Moscow, 1975).
35. T. S. Chihara, Introduction to Orthogonal Polynomials (Gordon and Breach, New York, 1978); G. Szegö, Orthogonal Polynomials (American Mathematical Society, New York, 1959, 4th ed.; Inostrannaya Literatura, Moscow, 1975).
36. Ya. I. Geronimus, Izv. Akad. Nauk SSSR, Ser. Fiz. 4, 215(1940).
37. A. A. Suzko, in Proceedings of the Seminar "Symmetries and Integrable Systems," Dubna, 1999, Ed. by A. N. Sissakian, p. 258; Preprint ESI-665 (1999).
38. V. E. Zakharov and A. B. Shabat, Fund. Anal. Appl. 8, 226(1974); 13, 166(1979).
39. V. E. Zakharov and A. B. Shabat, Fund. Anal. Appl. 8, 226(1974); 13, 166(1979).