An inverse scattering scheme for the regularized long-wave equation

Journal of Mathematical Physics

Volumn 41, Issue 5, 2000, Pages 2889-2904

  Dye, J M ^a   Parker, A ^a  

^a NEWCASTLE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347359     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533278     Document Type: Article

References (33)

1. D. J. Korteweg and G. de Vries, Philos. Mag. 39, 422-443 (1895).
2. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Phys. Rev. Lett. 19, 1095-1097 (1967).
3. C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, Commun. Pure Appl. Math. 27, 97-133 (1974).
4. D. H. Peregrine, J. Fluid Mech. 25, 321-330 (1966).
5. T. B. Benjamin, J. L. Bona, and J. J. Mahony, Philos. Trans. R. Soc. London, Ser. A 272, 47-78 (1972).
6. J. L. Bona, W. G. Pritchard, and L. R. Scott, Lect. Appl. Math. 20, 235-267 (1983).
7. P. G. Drazin and R. S. Johnson, Solitons: An Introduction (Cambridge U.P., Cambridge, England, 1990).
8. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981).
9. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Lond. Math. Soc. Lect. Note Ser. Vol. 149 (Cambridge U.P., Cambridge, England, 1991).
10. P. J. Olver, Math. Proc. Cambridge Philos. Soc. 85, 143-160 (1979).
11. D. K. Rollins, J. Math. Phys. 32, 3331-3332 (1991).
12. K. O. Abdulloev, I. L. Bogolubsky, and V. G. Makhankov, Phys. Lett. A 56, 427-428 (1976).
13. J. C. Eilbeck and G. R. McGuire, J. Comput. Phys. 23, 62-73 (1977).
14. A. R. Santarelli, Nuovo Cimento Soc. Ital. Fis., B 46, 176-188 (1978).
15. J. Courtenay Lewis and J. A. Tjon, Phys. Lett. A 73, 275-279 (1979).
16. J. L. Bona, W. G. Pritchard, and L. R. Scott, Phys. Fluids 23, 438-441 (1980).
17. J. B. Mcleod and P. J. Olver, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 14, 488-506 (1996).
18. A. C. Bryan and A. E. G. Stuart, J. Phys. Soc. Jpn. 65, 2417-2422 (1996).
19. M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, Stud. Appl. Math. 53, 249-315 (1974).
20. R. Hirota and J. Satsuma, J. Phys. Soc. Jpn. 40, 611-612 (1976).
21. A. Espinosa and J. Fujioka, J. Phys. Soc. Jpn. 63, 1289-1294 (1994).
22. J. Hietarinta, in Partially Integrable Evolution Equations in Physics, edited by R. Conte and N. Boccara (Kluwer, Netherlands, 1990).
23. A. Parker, J. Math. Phys. 36, 3498-3505 (1995).
24. V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl. 8, 226-235 (1974).
25. C. Van, J. Math. Phys. 34, 2618-2630 (1993).
26. P. D. Lax, Commun. Pure Appl. Math. 21, 467-490 (1968).
27. V. G. Makhankov, Phys. Rep. 35, 1-128 (1978).
28. R. S. Johnson and S. Thompson, Phys. Lett. A 66, 279-281 (1978).
29. A. R. Chowdhury and S. Basak, J. Phys. A 17, 863-868 (1984).
30. R. S. Johnson, in Nonlinear Dispersive Wave Systems, edited by L. Debnath (World Scientific, Singapore, 1992).
31. M. Musette and R. Conte, J. Math. Phys. 32, 1450-1457 (1991).
32. R. Hirota, J. Phys. Soc. Jpn. 58, 2705-2712 (1989).
33. P. Deift, C. Tomei, and E. Trubowitz, Commun. Pure Appl. Math. 35, 567-628 (1982).