Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability

Nonlinearity

Volumn 12, Issue 1, 1999, Pages 103-140

  Alexeeva, N V ^a   Barashenkov, I V ^a   Pelinovsky, D E ^b  

^a UNIVERSITY OF CRETE   (Greece)

^b UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032646251     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/12/1/007     Document Type: Article

References (53)

1. Juul Rasmussen J and Rypdal K 1986 Phys. Scr. 33 481 Turitsyn S K 1992 Singularities in Fluids, Plasmas and Optics (NATO ASI Series) ed R Caflisch (Dordrecht: Kluwer Academic)
2. Juul Rasmussen J and Rypdal K 1986 Phys. Scr. 33 481 Turitsyn S K 1992 Singularities in Fluids, Plasmas and Optics (NATO ASI Series) ed R Caflisch (Dordrecht: Kluwer Academic)
3. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
4. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
5. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
6. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
7. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
8. Eilbeck J C, Lomdahl P S and Newell A C 1981 Phys. Lett. A 87 1 Bishop A R, Fesser K, Lomdahl P S and Trullinger S E 1983 Physica D 7 259 Overman E A, McLaughlin D W and Bishop A R 1986 Physica D 19 1 Nozaki K and Bekki N 1983 Phys. Rev. Lett. 50 1226 Nozaki K and Bekki N 1984 Phys. Lett. A 102 383 Bishop A R, Forest M G, McLaughlin D W and Overman II E A 1986 Physica D 23 293
9. Umeki M 1991 J. Phys. Soc. Japan 60 146 Umeki M 1991 J. Fluid Mech. 227 161 Kambe J and Umeki M 1990 J. Fluid Mech. 212 373
10. Umeki M 1991 J. Phys. Soc. Japan 60 146 Umeki M 1991 J. Fluid Mech. 227 161 Kambe J and Umeki M 1990 J. Fluid Mech. 212 373
11. Umeki M 1991 J. Phys. Soc. Japan 60 146 Umeki M 1991 J. Fluid Mech. 227 161 Kambe J and Umeki M 1990 J. Fluid Mech. 212 373
12. Bondila M, Barashenkov I V and Bogdan M M 1995 Physica D 87 314
13. Barashenkov I V and Panova E Yu 1993 Physica D 69 114
14. Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103
15. Pelinovsky D E and Grimshaw R H J 1997 Nonlinear Instability Analysis (Advances in Fluid Mechanics) ed L Debnath and S Choudhury (Southampton: Computational Mechanics Publications) ch 8
16. Pelinovsky D E, Afanasjev V V and Kivshar Yu S 1996 Phys. Rev. E 53 1940 Pelinovsky D E, Kivshar Yu S and Afanasjev V V 1998 Physica D 116 121
17. Pelinovsky D E, Afanasjev V V and Kivshar Yu S 1996 Phys. Rev. E 53 1940 Pelinovsky D E, Kivshar Yu S and Afanasjev V V 1998 Physica D 116 121
18. Pelinovsky D E, Kivshar Yu S and Afanasjev V V 1996 Phys. Rev. E 54 2015
19. Barashenkov I V, Zhanlav T and Bogdan M M 1990 Nonlinear World: IY International Workshop on Nonlinear and Turbulent Processes in Physics (Kiev, 9-22 October 1989) ed V G Bar'yakhtar et al (Singapore: World Scientific) p 3 Terrones G, McLaughlin D W, Overman E A and Pearlstein A J 1990 SIAM J. Appl. Math. 50 791 Barashenkov I V and Smirnov Yu S 1996 Phys. Rev. E 54 5707
20. Barashenkov I V, Zhanlav T and Bogdan M M 1990 Nonlinear World: IY International Workshop on Nonlinear and Turbulent Processes in Physics (Kiev, 9-22 October 1989) ed V G Bar'yakhtar et al (Singapore: World Scientific) p 3 Terrones G, McLaughlin D W, Overman E A and Pearlstein A J 1990 SIAM J. Appl. Math. 50 791 Barashenkov I V and Smirnov Yu S 1996 Phys. Rev. E 54 5707
21. Barashenkov I V, Zhanlav T and Bogdan M M 1990 Nonlinear World: IY International Workshop on Nonlinear and Turbulent Processes in Physics (Kiev, 9-22 October 1989) ed V G Bar'yakhtar et al (Singapore: World Scientific) p 3 Terrones G, McLaughlin D W, Overman E A and Pearlstein A J 1990 SIAM J. Appl. Math. 50 791 Barashenkov I V and Smirnov Yu S 1996 Phys. Rev. E 54 5707
22. Barashenkov I V, Bogdan M M and Korobov V I 1991 Europhys. Lett. 15 113
23. Pego R L, Smereka P and Weinstein M I 1995 Nonlinearity 8 921
24. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
25. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
26. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
27. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
28. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
29. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
30. Wu J, Keolian R and Rudnick I 1984 Phys. Rev. Lett. 52 1421 Laedke E W and Spatschek K H 1991 J. Fluid. Mech. 223 589 Yan J R and Mei Y P 1993 Europhys. Lett. 23 335 Chen X-N and Wei R-J 1994 J. Fluid Mech. 259 291 Wang X and Wei R 1994 Phys. Lett. A 192 1 Wang X and Wei R 1997 Phys. Lett. A 227 55 Wang X and Wei R 1997 Phys. Rev. Lett. 78 2744
31. Miles J W 1984 J. Fluid Mech. 148 451
32. Zakharov V E, Musher S L and Rubenchik A M 1985 Phys. Rep. 129 285 Yajima N and Tanaka M 1988 Prog. Theor. Phys. Suppl. 94 138
33. Zakharov V E, Musher S L and Rubenchik A M 1985 Phys. Rep. 129 285 Yajima N and Tanaka M 1988 Prog. Theor. Phys. Suppl. 94 138
34. Zakharov V E, L'vov V S and Starobinets S S 1975 Sov. Phys.-Usp. 17 896 L'vov V S et al 1973 Fizika Tverdogo Tela 15 793 Yamazaki H and Mino M 1989 Prog. Theor. Phys. Suppl. 98 400
35. Zakharov V E, L'vov V S and Starobinets S S 1975 Sov. Phys.-Usp. 17 896 L'vov V S et al 1973 Fizika Tverdogo Tela 15 793 Yamazaki H and Mino M 1989 Prog. Theor. Phys. Suppl. 98 400
36. Zakharov V E, L'vov V S and Starobinets S S 1975 Sov. Phys.-Usp. 17 896 L'vov V S et al 1973 Fizika Tverdogo Tela 15 793 Yamazaki H and Mino M 1989 Prog. Theor. Phys. Suppl. 98 400
37. Bogdan M M, Kosevich A M and Manzhos I V 1985 Sov. J. Low Temp. Phys. 11 547
38. Deutsch I H and Abram I 1994 J. Opt. Soc. Am. B 11 2303 Longhi S 1995 Opt. Lett. 20 695 Mecozzi A, Kath L, Kumar P and Goedde C G 1994 Opt. Lett. 19 2050
39. Deutsch I H and Abram I 1994 J. Opt. Soc. Am. B 11 2303 Longhi S 1995 Opt. Lett. 20 695 Mecozzi A, Kath L, Kumar P and Goedde C G 1994 Opt. Lett. 19 2050
40. Deutsch I H and Abram I 1994 J. Opt. Soc. Am. B 11 2303 Longhi S 1995 Opt. Lett. 20 695 Mecozzi A, Kath L, Kumar P and Goedde C G 1994 Opt. Lett. 19 2050
41. Pagano S, Salerno M and Samuelsen M R 1987 Physica D 26 396 Grønbech-Jensen N, Kivshar Y S and Samuelsen M R 1993 Phys. Rev. B 47 5013 Grauer R and Kivshar Y S 1993 Phys. Rev. E 48 4791
42. Pagano S, Salerno M and Samuelsen M R 1987 Physica D 26 396 Grønbech-Jensen N, Kivshar Y S and Samuelsen M R 1993 Phys. Rev. B 47 5013 Grauer R and Kivshar Y S 1993 Phys. Rev. E 48 4791
43. Pagano S, Salerno M and Samuelsen M R 1987 Physica D 26 396 Grønbech-Jensen N, Kivshar Y S and Samuelsen M R 1993 Phys. Rev. B 47 5013 Grauer R and Kivshar Y S 1993 Phys. Rev. E 48 4791
44. Guckenheimer J and Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Berlin: Springer) Marsden J and McCracken M 1976 The Hopf Bifurcation and Its Applications (Berlin: Springer)
45. Guckenheimer J and Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Berlin: Springer) Marsden J and McCracken M 1976 The Hopf Bifurcation and Its Applications (Berlin: Springer)
46. Weideman J A C and Herbst B M 1986 SIAM J. Numer. Anal. 23 485
47. Kosevitch A M and Kovalev A S 1974 Zh. Eksper. Teoret. Fiz. 67 1793 (Engl. transl. 1974 Sov. Phys.-JETP 40 891) Dashen R F, Hasslacher B and Neveu A 1974 Phys. Rev. D 10 4130 Segur H and Kruskal M D 1987 Phys. Rev. Lett. 58 747 Boyd J P 1990 Nonlinearity 3 177
48. Kosevitch A M and Kovalev A S 1974 Zh. Eksper. Teoret. Fiz. 67 1793 (Engl. transl. 1974 Sov. Phys.-JETP 40 891) Dashen R F, Hasslacher B and Neveu A 1974 Phys. Rev. D 10 4130 Segur H and Kruskal M D 1987 Phys. Rev. Lett. 58 747 Boyd J P 1990 Nonlinearity 3 177
49. Kosevitch A M and Kovalev A S 1974 Zh. Eksper. Teoret. Fiz. 67 1793 (Engl. transl. 1974 Sov. Phys.-JETP 40 891) Dashen R F, Hasslacher B and Neveu A 1974 Phys. Rev. D 10 4130 Segur H and Kruskal M D 1987 Phys. Rev. Lett. 58 747 Boyd J P 1990 Nonlinearity 3 177
50. Kosevitch A M and Kovalev A S 1974 Zh. Eksper. Teoret. Fiz. 67 1793 (Engl. transl. 1974 Sov. Phys.-JETP 40 891) Dashen R F, Hasslacher B and Neveu A 1974 Phys. Rev. D 10 4130 Segur H and Kruskal M D 1987 Phys. Rev. Lett. 58 747 Boyd J P 1990 Nonlinearity 3 177
51. Kosevitch A M and Kovalev A S 1974 Zh. Eksper. Teoret. Fiz. 67 1793 (Engl. transl. 1974 Sov. Phys.-JETP 40 891) Dashen R F, Hasslacher B and Neveu A 1974 Phys. Rev. D 10 4130 Segur H and Kruskal M D 1987 Phys. Rev. Lett. 58 747 Boyd J P 1990 Nonlinearity 3 177
52. Bondila M 1995 MSc Thesis University of Cape Town, unpublished
53. Longhi S 1997 Phys. Rev. E 55 1060