Bifurcation of internal solitary wave modes from the essential spectrum

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 3, 2000, Pages 3114-3121

  Kevrekidis, P G ^a   Jones, C K R T ^b  

^a RUTGERS UNIVERSITY   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); NUMERICAL METHODS; SOLITONS;

CONTINUUM APPROXIMATION; CONTINUUM EQUATION; ESSENTIAL SPECTRUM; INTERNAL SOLITARY WAVES; NUMERICAL COMPUTATIONS; PERTURBATION THEORY; SEMI-ANALYTICAL TECHNIQUES; SOLI-TARY WAVE SOLUTIONS;

PERTURBATION TECHNIQUES;

EID: 0001496277     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.3114     Document Type: Article

References (37)

1. A.V. Ustinov, T. Doderer, I.V. Vernik, N.F. Pedersen, R.P. Huebener, and V.A. Oboznov, Physica D 68, 41 (1994).
2. T. Holst, L.E. Guettero, N. Gronbech-Jensen, J.A. Blackburn, and J. Bindlev-Hansen, Superconducting Devices and their Applications (Springer-Verlag, Berlin, 1992).
3. K. Xu, D. Lu, and X. Yao, Chin. J. Low Temp. Phys. 14, 293 (1992).
4. J. Kutz, C. Hile, W. Kath, R.-D. Li, and P. Kummar, J. Opt. Soc. Am. B 11, 2112 (1994).
5. J. Kutz, C. Hile, W. Kath, R.-D. Li, and P. Kummar, Opt. Lett. 18, 802 (1993).
6. M. Peyrard and A.R. Bishop, Phys. Rev. Lett. 62, 2755 (1989).
7. T. Dauxois, Phys. Lett. A 159, 390 (1991).
8. T. Dauxois, M. Peyrard, and C.R. Willis, Physica D 57, 267 (1992).
9. T. Dauxois, M. Peyrard, and A.R. Bishop, Physica D 66, 35 (1993).
10. X. Yang, Y. Zhuo, and X. Wu, Phys. Lett. A 234, 152 (1997).
11. J. Frenkel and T. Kontorova, J. Phys. USSR 1, 137 (1939).
12. J.H. Heiner, Phys. Rev. A 136, 863 (1964).
13. W. Atkinson and N. Cabrera, Phys. Rev. A 138, 763 (1965).
14. D.E. Pelinovsky and S.Kh. Shavratsky, Physica D 1, 317 (1980).
15. M. Peyrard and M.D. Kruskal, Physica D 14, 88 (1984).
16. Y. Ishimori and T. Munakata, J. Phys. Soc. Jpn. 51, 3367 (1982).
17. J.A. Combs and S. Yip, Phys. Rev. B 28, 6873 (1983).
18. P.G. Kevrekidis and M.I. Weinstein (unpublished).
19. R. Boesch, C.R. Willis, and M. El-Batanouny, Phys. Rev. B 40, 2284 (1989).
20. R. Boesch and C.R. Willis, Phys. Rev. B 39, 361 (1989).
21. N.J. Balmforth, R.C. Craster, and P.G. Kevrekidis, Physica D 135, 212 (2000).
22. C. Willis, M. El-Batanouny, and P. Stancioff, Phys. Rev. B 33, 1904 (1986).
23. P. Stancioff, C. Willis, M. El-Batanouny, and S. Burdick, Phys. Rev. B 33, 1912 (1986).
24. R. Boesch, P. Stancioff, and C.R. Willis, Phys. Rev. B 38, 6713 (1988).
25. C.R. Willis and R. Boesch, Phys. Rev. B 41, 4570 (1990).
26. R. Boesch and C.R. Willis, Phys. Rev. B 42, 6371 (1990).
27. O.M. Braun, Yu.S. Kivshar, and M. Peyrard, Phys. Rev. E 56, 6050 (1997).
28. Yu.S. Kivshar, D.E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
29. T. Kapitula and B. Sandstede (unpublished), available at http://www.math.unm.edu/ kapitula
30. T. Kapitula and B. Sandstede (unpublished)available at http://www.math.unm.edu/ kapitula.
31. A.R. Bishop, S.E. Trullinger, and J.A. Krumhansl, Physica D 1, 1 (1980).
32. R.L. Pego and M.I. Weinstein, Philos. Trans. R. Soc. London, Ser. A 340, 47 (1992).
33. T. Kapitula, SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 30, 273 (1999).
34. R.L. Pego and M.I. Weinstein, in Mathematics in Science and Engineering, edited by W.F. Ames, E.M. Harrell II, and J.V. Herod (Academic, Orlando, 1993), Vol. 192.
35. S. Chow, J. Hale, and J. Mallet-Paret, J. Diff. Eqns. 37, 351 (1980).
36. J.P. Keener and D.W. McLaughlin, Phys. Rev. A 16, 777 (1977).
37. D.W. McLaughlin and A.C. Scott, Phys. Rev. A 18, 1652 (1978).