On preliminary symmetry classification of nonlinear schrödinger equations with some applications to doebner-goldin models

Reports on Mathematical Physics

Volumn 45, Issue 2, 2000, Pages 273-291

  Zhdanov, Renat ^a   Roman, Olena ^b  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b CLAUSTHAL UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034164994     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0034-4877(00)89037-0     Document Type: Article

References (24)

1. I. Białynicki-Birula and J. Mycielski: Ann. Phys. (N.Y.) 100 (1976), 62-74.
2. H.-D. Doebner and G. A. Goldin: Phys. Lett. A 162 (1992), 397-401.
3. H.-D. Doebner and G. A. Goldin: J. Phys. A: Math. Gen. 27 (1994), 1771-1780.
4. T. W. B. Kibble: Commun. Math. Phys. 64 (1978), 73-82.
5. F. Guerra and M. Pusterla: Lett. Nuovo Cim. 34 (1982), 351-356.
6. L. Smolin: Phys. Lett. A 113 (1986), 408-412.
7. J.-P. Vigier: Phys. Lett. A. 135 (1989), 99-105.
8. P. C. Sabatier: Inverse Problems 6 (1990), L47-L53.
9. O. Bertolami: Phys. Lett. A 154 (1991), 225-229.
10. P. Nattermann: Rep. Math. Phys. 36 (1995), 387-396.
11. P. Nattermann and R. Z. Zhdanov: J. Phys. A: Math. Gen. 29 (1996), 2869-2886.
12. L. V. Ovsjannikov: Group Analysis of Differential Equations, Academic Press, New York 1982.
13. P. J. Olver: Applications of Lie Groups to Differential Equations, Springer, Berlin 1996.
14. N. Jacobson: Lie Algebras, Dover Publications, New York 1979.
15. G. M. Mubarakzyanov: Izvestiya Vysshykh Uchebnykh Zavedenij. Matematika 32 (1963), 114-123.
16. G. M. Mubarakzyanov: Izvestiya Vysshykh Uchebnykh Zavedenij. Matematika 34 (1963), 99-106.
17. P. Turkowski: J. Math. Phys. 29 (1988), 2139-14.
18. R. Z. Zhdanov and V. I. Lahno: Group Classification of Heat Conductivity Equations with a Nonlinear Source, math-ph/9906003.
19. I. S. Akhatov, R. K. Gazizov and N. K. Ibragimov: Sovremennye Problemy Matematiki. Novejshie DosTizheniya 34, Nauka, Moscow 1989, 3-83.
20. G. Rideau and P. Winternitz: J. Math. Phys. 34 (1993), 558-570.
21. R. Z. Zhdanov and W. I. Fushchych: J. Non. Math. Phys. 4, (1997), 426-435.
22. W. I. Fushchych and V. I. Lahno: Ukrain. Math. J. 51 (1999), 341-349.
23. F. Güngör: J. Phys. A: Math. Gen. 32 (1999), 977-988.
24. U. Niederer: Helv. Phys. Acta 45, (1972), 802-810.