Perturbative analysis of wave interaction in nonlinear systems

Theoretical and Mathematical Physics

Volumn 144, Issue 2, 2005, Pages 1227-1237

  Veksler, A ^a   Zarmi, Y ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Nonlinear evolution equations; Obstacles to asymptotic integrability; Perturbed Burgers equation; Perturbed KdV equation; Wave interaction

Indexed keywords

EID: 23944514116     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11232-005-0154-2     Document Type: Conference Paper

References (31)

1. D. J. Kaup, SIAM J. Appl. Math., 31, 121 (1976).
2. D. J. Kaup and A. S. Newell, Proc. Roy. Soc. London A, 361, 413 (1978).
3. V. I. Karpman and E. M. Maslov, JETP, 46, 281 (1977).
4. A. C. Newell, "The inverse scattering transform," in: Solitons (R. K. Bullough and P. J. Caudrey, eds.), Springer, Berlin (1980), p. 177.
5. L. A. Kalyakin, Russ. Math. Surveys, 44, 3 (1989).
6. L. A. Kalyakin, Theor. Math. Phys., 92, 736 (1992).
7. L. A. Kalyakin, Phys. D, 87, 193 (1995).
8. L. A. Kalyakin and V. A. Lazarev, Theor. Math. Phys., 112, 866 (1997).
9. Y. Kodama, Phys. Lett. A, 112, 193 (1985).
10. Y. Kodama, Phys. D, 16, 14 (1985).
11. Y. Kodama, "Normal form and solitons," in: Topics in Soliton Theory and Exactly Solvable Nonlinear Equations (Proc. Conf. on Nonlinear Evolution Equations, Solitons, and the Inverse Scattering Transform, Oberwolfach, Germany, July 27-August 2, 1986, M. J. Ablowitz, B. Fuchssteiner, and M. Kruskal, eds.), World Scientific, Singapore (1987), p. 319.
12. Y. Kodama and A. V. Mikhailov, "Obstacles to asymptotic integrability," in: Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman (Progr. Nonlinear Diff. Eq. and their Appl., Vol. 26, A. S. Fokas and I. M. Gelfand, eds.), Birkhäuser, Boston (1997), p. 173.
13. Y. Hiraoka and Y. Kodama, Normal Form and Solitons (Lecture Notes, Euro Summer School 2001, The Isaac Newton Institute, Cambridge, August 15-25) (unpublished).
14. Y. Kodama and T. Taniuti, J. Phys. Soc. Japan, 47, 1706 (1979).
15. T. Fokas and L. Luo, Contemp. Math., 200, 85 (1996).
16. R. A. Kraenkel, J. G. Pereira, and E. C. de Rey Neto, Phys. Rev. E, 58, 2526 (1998).
17. R. A. Kraenkel, M. A. Manna, V. Merle, J. C. Montero, and J. G. Pereira, Phys. Rev. E, 54, 2976 (1996).
18. R. A. Kraenkel, Phys. Rev. E, 57, 4775 (1998).
19. R. A. Kraenkel, M. Senthilvelan, and A. I. Zenchuk, J. Math. Phys., 41, 3160 (2000).
20. A. Degasperis, S. V. Manakov, and P. M. Santini, Phys. D, 100, 187 (1997).
21. Y. Kodama and T. Taniuti, J. Phys. Soc. Japan, 45, 298 (1978).
22. Y. Kodama, J. Phys. Soc. Japan, 45, 311 (1978).
23. B. Fuchssteiner and A. S. Fokas, Phys. D, 4, 47 (1981).
24. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering, Cambridge Univ. Press, Cambridge (1991).
25. H. Tasso, J. Phys. A, 29, 7779 (1996).
26. A. S. Fokas, R. H. J. Grimshaw, and D. E. Pelinovsky, J. Math. Phys., 37, 3415 (1996).
27. Y. Kodama, Phys. Lett. A, 123, 276 (1987).
28. R. Hirota, Phys. Rev. Lett., 27, 1192 (1971).
29. J. P. Keener and D. W. McLaughlin, Phys. Rev. A, 16, 777 (1977).
30. R. L. Sachs, SIAM J. Math. Anal., 14, 674 (1983).
31. R. L. Sachs, SIAM J. Math. Anal., 15, 468 (1984).