Existence and stability chart for the ac-driven, damped nonlinear Schrödinger solitons

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

Volumn 54, Issue 5, 1996, Pages 5707-5725

  Barashenkov, I V ^a   Smirnov, Yu S ^a  

^a UNIVERSITY OF CAPE TOWN   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001532443     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.54.5707     Document Type: Article

References (35)

1. D J. Kaup and A C. Newell, Proc. R. Soc. London Ser. A361, 413 (1978).
2. D J. Kaup and A C. Newell, Phys. Rev. B18, 5162 (1978).
3. J C. Eilbeck, P S. Lomdahl and A C. Newell, Phys. Lett.87A, 1 (1981);
4. D. Bennett, A R. Bishop and S E. Trullinger, Z. Phys. B47, 265 (1982);
5. A R. Bishop, K. Fisser, P S. Lomdahl, W C. Kerr, M B. Williams and S E. Trullinger, Phys. Rev. Lett.50, 1095 (1983);
6. A R. Bishop, K. Fesser, P S. Lomdahl and S E. Trullinger, Physica D7, 259 (1983).
7. E A. Overman, D W. McLaughlin and A R. Bishop, Physica D19, 1 (1986).
8. K. Nozaki and N. Bekki, Phys. Rev. Lett.50, 1226 (1983);
9. K. Nozaki and N. Bekki, Phys. Lett.102A, 383 (1984).
10. K. Nozaki and N. Bekki, J. Phys. Soc. Jpn.54, 2363 (1985).
11. K. Nozaki and N. Bekki, Physica D21, 381 (1986).
12. A R. Bishop, M G. Forest, D W. McLaughlin and E A. Overman, Physica D23, 293 (1986).
13. A. Mazor, A R. Bishop and D W. McLaughlin, Phys. Lett. A119, 273 (1986);
14. A. Mazor and A R. Bishop, Physica D27, 269 (1987).
15. M. Taki, K H. Spatschek, J C. Fernandez, R. Grauer and G. Reinisch, Physica D40, 65 (1989).
16. K. H. Spatschek, H. Pietsch, E. W. Laedke, and Th. Eickermann, in Singular Behaviour and Nonlinear Dynamics, edited by T. Bountis and St. Pnevmatikos (World Scientific, Singapore, 1989).
17. R. Grauer and B. Birnir, Physica D56, 165 (1992).
18. Th. Eickermann, R. Grauer and K H. Spatschek, Phys. Lett. A198, 383 (1995).
19. I V. Barashenkov, M M. Bogdan, and T. Zhanlav, in Nonlinear World, Proceedings of the Fourth International Workshop on Nonlinear and Turbulent Processes in Physics, Kiev, 1989, edited by V. G. Bar'yakhtar (World Scientific, Singapore, 1990), p. 3.
20. G. Terrones, D W. McLaughlin, E A. Overman and A J. Pearlstein, SIAM J. Appl. Math.50, 791 (1990).
21. I V. Barashenkov, M M. Bogdan and V I. Korobov, Europhys. Lett.15, 113 (1991).
22. M. Bondila, I V. Barashenkov and M M. Bogdan, Physica D87, 314 (1995).
23. The formation of soliton bound states was studied within the perturbative framework;
24. see B A. Malomed, Phys. Rev. A44, 6954 (1991);
25. B A. Malomed, Phys. Rev. A45, 8321 (1992);
26. B A. Malomed, Phys. Rev. E47, 2874 (1993)
27. D. Cai, A R. Bishop, N. Grønbech-Jensen and B A. Malomed, Phys. Rev. E49, 1677 (1994).
28. Two underlying assumptions were that (i) h and γ are small and (ii) the separation between solitons is large. The possibility of bound states to occur for finite h and γ is an open question, however, as well as whether strongly overlapping solitons may bind together.
29. The continuous analog of Newton's method (also known as the variable iteration step Newton method) was formulated by M. K. Gavurin, Izv. Vuzov Mat. 5-6, 18 (1958).
30. For reviews see, e.g., E P. Zhidkov, G I. Makarenko and I V. Puzynin, Fiz. Elem. Chastits At. Yadra4, 127 (1973) [Sov. J. Part. Nucl.4, 53 (1973)];
31. L. Bracci and G. Fiorentini, Phys. Rep.86, 170 (1982).
32. Recent advances are discussed by T. Zhanlav and I V. Puzynin, Comp. Math. Math. Phys.32, 729 (1992);
33. T. Zhanlav and I V. Puzynin, Comp. Math. Math. Phys.32, 1 (1993);
34. T. Zhanlav and I V. Puzynin, Comp. Math. Math. Phys.34, 143 (1994).
35. The procedure of the optimal iteration step choice that we follow was suggested by V V. Ermakov and N N. Kalitkin, Zh. Vych. Mat. Mat. Fiz.21, 491 (1981).