Initial-boundary value problems for linear and soliton PDEs

Theoretical and Mathematical Physics

Volumn 133, Issue 2, 2002, Pages 1475-1489

  Degasperis, A ^a   Manakov, S V ^b   Santini, P M ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

Boundary conditions; Integrability; Solitons

Indexed keywords

EID: 0036437259     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021138525261     Document Type: Conference Paper

References (25)

1. P. M. Morse and H. Feehbach, Methods of Theoretical Physics, McGraw-Hill, New York (1953).
2. R. Terrae and R. Swanson, J. Math. Phys., 21, 2140 (1980).
3. A. S. Fokas, Proc. Roy. Soc. London A, 53, 1411 (1997).
4. A. S. Fokas, J. Math. Phys., 41, 4188 (2000).
5. A. S. Fokas, Proc. Roy. Soc. London A, 457, 371 (2001).
6. A. S. Fokas and B. Pelloni, Math. Proc. Camb. Phil. Soc., 131, 521 (2001).
7. B. Pelloni, Theor. Math. Phys., 133, 1598 (2002).
8. A. Degaeperis, S. V. Manakov, and P. M. Santini, "Initial-boundary value problems for linear PDEs: The analyticity approach," nlin.SI/0210058 (2002).
9. A. S. Fokas, "Inverse scattering transform on the half line - the nonlinear analogue of the sine transform," in: Inverse Problems: An Interdisciplinary Study (P. C. Sabatier, ed.), Acad. Press, London (1987), p. 409.
10. P. C. Sabatier, J. Math. Phys., 41, 414 (2000).
11. A. S. Fokas, A. R. Its, and L. Y. Sung, "The nonlinaer Schrödinger equation on the half-line," Preprint, Cambridge Univ. Press, Cambridge (2001).
12. A. S. Fokas, "Integrable nonlinear evolution equations on the half-line (October 2001)," Comm. Math. Phys. (to appear).
13. A. S. Fokas and A. R. Its, Phys. Rev. Lett., 68, 3117 (1992).
14. M. J. Ablowitz and H. Segur, J. Math. Phys., 16, 1054 (1975).
15. A. Degasperis, S. V. Manakov, and P. M. Santini, JETP Letters, 74, 481 (2001).
16. I. T. Khabibullin, Theor. Math. Phys., 130, 25 (2002).
17. J. Leon and A. V. Mikhailov, Phys. Lett. A, 253, 33 (1999).
18. J. Leon and A. Spire, J. Phys. A, 34, 7359 (2001); nlin.PS/0105066 (2001).
19. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981); V. E. Zakhatov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakhatov, Plenum, New York (1984).
20. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981); V. E. Zakhatov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakhatov, Plenum, New York (1984).
21. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia (1981); V. E. Zakhatov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakhatov, Plenum, New York (1984).
22. A. C. Newell, "The inverse scattering transform," in: Solitons (R. K. Bullough and P. J. Caudrey, eds.), Springer, Berlin (1980), p. 177.
23. F. Calogero and S. De Lillo, Inverse Problems, 4, L33, (1988); J. Math. Phys., 32, 99 (1991); M. J. Ablowitz and S. De Lillo, Phys. Lett. A, 156, 483 (1991).
24. F. Calogero and S. De Lillo, Inverse Problems, 4, L33, (1988); J. Math. Phys., 32, 99 (1991); M. J. Ablowitz and S. De Lillo, Phys. Lett. A, 156, 483 (1991).
25. F. Calogero and S. De Lillo, Inverse Problems, 4, L33, (1988); J. Math. Phys., 32, 99 (1991); M. J. Ablowitz and S. De Lillo, Phys. Lett. A, 156, 483 (1991).