Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 323, Issue 3-4, 2004, Pages 241-250

  Nieszporski, M ^a,b   Santini, P M ^c   Doliwa, A ^d  

^a UNIVERSITY OF WARSAW   (Poland)

^b UNIVERSITY OF BIALYSTOK   (Poland)

^c UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^d UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN   (Poland)

Author keywords

04.60.Nc; Darboux transformations; Difference equations; Lattice integrable nonlinear models

Indexed keywords

DIFFERENCE EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

04.60.NC; ADJOINTS; DARBOUX TRANSFORMATIONS; DIFFERENCE SCHEMES; DINGER EQUATION; DISCRETIZATIONS; ELLIPTIC PARTIAL DIFFERENTIAL EQUATION;

NONLINEAR EQUATIONS;

ARTICLE; GEOMETRY; MATHEMATICAL ANALYSIS; OPERATOR; SPECTROSCOPY;

EID: 1542315521     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2004.02.003     Document Type: Article

References (29)

1. Matveev V.B., Salle M.A. Darboux Transformations and Solitons. Springer Series in Nonlinear Dynamics. 1991;Springer-Verlag, Berlin.
2. Ablowitz M.J., Segur H. Solitons and the Inverse Scattering Transform. 1981;SIAM, Philadelphia.
3. Manakov S.V., Novikov S.P., Pitaevskii L.P., Zakharov V.E. Theory of Solitons: The Inverse Scattering Method. 1984;Consultants Bureau, New York.
4. Suris Y.B. R-matrices and integrable discretization. Discrete Integrable Geometry and Physics. 1999;Clarendon Press, Oxford.
5. Novikov S.P. Russian Math. Surveys. 52:1997;226.
6. Novikov S.P., Dynnikov I.A. Russian Math. Surveys. 52:1997;1057.
7. Veselov A.P., Novikov S.P. Soviet Math. Dokl. 30:1984;588.
8. Misner C.W. Phys. Rev. D. 18:1978;4510.
9. Ernst F.J. Phys. Rev. 167:1968;1175.
10. Toda M. Theory of Nonlinear Lattices. Springer Series in Solid-State Sciences. vol. 20:1981;Springer, Berlin.
11. Jonas H. Berlin Sitzungsber. XIV:1915;96.
12. Eisenhart L.P. Transformation of Surfaces. 1923;Princeton Univ. Press, Princeton, NJ.
13. Bogdanov L.V., Konopelchenko B.G. J. Phys. A: Math. Gen. 28:1995;L173.
14. Doliwa A. Phys. Lett. A. 234:1997;187.
15. Doliwa A., Santini P.M. Phys. Lett. A. 233:1997;365.
16. Manas M., Doliwa A., Santini P.M. Phys. Lett. A. 232:1997;99.
17. Konopelchenko B.G., Schief W.K. Proc. R. Soc. London A. 454:1998;3075.
18. Doliwa A., Santini P.M., Manas M. J. Math. Phys. 41:2000;944.
19. Adler V.E., Startsev S.Ya. Theor. Math. Phys. 121:1999;1484.
20. Moutard Th.-F. J. Ec. Pol. 45:1878;1.
21. Nimmo J.J.C., Schief W.K. Proc. R. Soc. London A. 453:1997;255.
22. Nieszporski M. Theor. Math. Phys. 133:2002;1576.
23. Grundland M., Levi D., Martina L. J. Phys. A: Math. Gen. 36:2003;4599.
24. Hildebrand F.B. Finite Difference Equations and Simulations. 1968;Prentice-Hall, Englewood Cliffs.
25. Dynnikov I.A., Novikov S.P. math-ph/0208041.
26. Flaschka H. Prog. Theor. Phys. 51:1974;703.
27. Manakov S.V. Soviet Phys. JETP. 40:1975;269.
28. Schief W.K. Appl. Math. Lett. 10:1997;13.
29. Shabat A. Boiti M., Martina L., Pempinelli F., Prinari B., Soliani G. Nonlinearity, Integrability and All That. Twenty Years After NEEDS'79. 2000;331 World Scientific, Singapore.