Squared Eigenfunction Symmetries for Soliton Equations: Part I

Journal of Mathematical Analysis and Applications

Volumn 217, Issue 1, 1998, Pages 161-178

  Oevel, Walter ^a   Carillo, Sandra ^b  

^a UNIVERSITY OF PADERBORN   (Germany)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Integrable systems; squared eigenfunctions; B cklund transformations; KP hierarchy; modified KP hierarchy; Dym hierarchy

Indexed keywords

EID: 84903362336     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5707     Document Type: Article

References (28)

1. Adler M. On a trace functional for pseudo differential operators and the symplectic structure of the Korteweg-de Vries equation. Invent. Math. 50:1979;219-248.
2. Aratyn H., Nissimov E., Pacheva S., Vaysburd I. R. Phys. Lett. B. 294:1992;167-176.
3. Calogero F., Degasperis A. Spectral transform and solitons I. Stud. Math. Appl. 13:1982.
4. Carillo S., Fuschssteiner B. The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links. J. Math. Phys. 30:1989;1606-1613.
5. Cheng Y. Constraints of the KP hierarchy. J. Math. Phys. 33:1992;3774-3782.
6. Fokas A. S., Ablowitz M. J. On the inverse scattering transform of the time dependent Schrödinger equation and the associated Kadomtsev-Petviashvili (I) equation. Stud. Appl. Math. 69:1983;211-228.
7. Fokas A. S., Fuchssteiner B. Bäcklund transformations for hereditary symmetries. Nonlinear Anal. TMA. 5:1981;423-432.
8. Fuchssteiner B., Carillo S. Soliton structure versus singularity analysis: third order completely integrable nonlinear equations in 1 + 1 dimensions. Phys. A. 152:1989;467-510.
9. Gelfand I. M., Dikii L. A. Fractional powers of operators and Hamiltonian systems. Funct. Anal. Appl. 10:1976;259-273.
10. Kiso K. A remark on the commuting flows defined by Lax equations. Prog. Theor. Phys. 83:1990;1108-1114.
11. Konopelchenko B. G., Dubrovsky V. G. Some new integrable nonlinear evolution equations in 2 + 1 dimensions. Phys. Lett. A. 102:1984;15-17.
12. Konopelchenko B. G., Oevel W. Anr. Publ. Res. Inst. Math. Sci. 29:1993;581-666.
13. Konopelchenko B. G., Rogers C. Bäcklund and reciprocal transformations: Gauge connections. Ames W. F., Rogers C. Nonlinear Equations in the Applied Sciences. 1992;317-362 Academic Press, Boston.
14. Konopelchenko B. G., Schief W., Rogers C. A (2 + 1)-dimensional sine-Gordon system: its auto-Bäcklund transformation. Phys. Lett. A. 172:1992;39-49.
15. Konopelchenko B. G., Sidorenko J., Strampp W. (1 + 1)-dimensional integrable systems as symmetry constraint of (2 + 1)-dimensional systems. Phys. Lett. A. 157:1991;17-21.
16. Konopelchenko B. G., Strampp W. The AKNS hierarchy as symmetry constraint of the KP hierarchy. Inverse Problems. 7:1991;L17-L24.
17. W. Oevel, S. Carillo, Squared eigenfunction symmetries for soliton equations: Part II.
18. Oevel W., Rogers C. Gauge transformation and reciprocal links in 2 + 1 dimensions. Rev. Math. Phys. 5:1993;299-330.
19. Oevel W., Schief W. Squared eigenfunctions of the (modified) KP hierarchy and scattering problems of Loewner type. Rev. Math. Phys. 6:1994;1301-1338.
20. Ohta Y., Satsuma J., Takahashi D., Tokihiro T. An elementary introduction to Sato theory. Prog Theor. Phys. Suppl. 94:1988;210-241.
21. Rogers C. The Harry Dym equation in 2 + 1 dimensions: A reciprocal link with the Kadomtsev-Petviashvili equation. Phys. Lett. A. 120:1987;15-18.
22. Rogers C., Ames W. F. Nonlinear Boundary Value Problems in Science and Engineering. 1989;Academic Press, Boston.
23. Rogers C., Shadwick W. F. Bäcklund transformations and their applications. Math. Sci. and Eng. 161:1982.
24. Rogers C., Wong P. On reciprocal Bäcklund transformations and the Korteweg-de Vries hierarchy. Phys. Scr. 30:1984;10-14.
25. Semenov-Tian-Shansky M. A. What is a classicalR. Funct. Anal. Appl. 17:1983;259-272.
26. Weiss C. Painlevé property for partial differential equations II: Bäcklund transformations, Lax pairs and the Schwarzian derivative. J. Math. Phys. 24:1983;1405-1413.
27. Weiss C. Bäcklund transformation and Painlevé-property. J. Math. Phys. 27:1986;1293-1305.
28. Xu B. (1 + 1)-dimensional integrable Hamiltonian systems reduced from symmetry constraints of the KP hierarchy. Inverse Problems. 9:1993;355-363.