Focusing revisited: A renormalization/bifurcation approach

Nonlinearity

Volumn 16, Issue 2, 2003, Pages 497-506

  Siettos, C I ^a   Kevrekidis, I G ^a   Kevrekidis, P G ^b  

^a Princeton University   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0043129307     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/2/308     Document Type: Article

References (38)

1. Sulem C and Sulem P L 1999 The Nonlinear Schrödinger Equation (New York: Springer)
2. Juul Rasmussen J and Rypdal K 1986 Phys. Scr. 33 481
3. Barenblatt G I 1996 Scaling, Self-Similarity and Intermediate Asymptotics (Cambridge: Cambridge University Press)
4. Choptuik M W 1993 Phys. Rev. Lett. 70 9 Koike T, Hara T and Adaehi S 1995 Phys. Rev. Lett. 74 5170
5. Choptuik M W 1993 Phys. Rev. Lett. 70 9 Koike T, Hara T and Adaehi S 1995 Phys. Rev. Lett. 74 5170
6. Bergé L 1998 Phys. Rep. 303 259
7. Goldenfeld N 1992 Lectures on Phase Transitions and the Renomalization Group (Boston, MA: Addison- Wesley)
8. Brenner M P et al 1999 Nonlinearity 12 1071
9. LeMesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1986 Phys. D 31 78 LeMesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1988 Phys. D 32 210
10. LeMesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1986 Phys. D 31 78 LeMesurier B J, Papanicolaou G C, Sulem C and Sulem P L 1988 Phys. D 32 210
11. McLaughlin D W, Papanicolaou G C, Sulem C and Sulem P L 1986 Phys. Rev. A 34 1200
12. Landman M J, Papanicolaou G C, Sulem C and Sulem P L 1988 Phys. Rev. A 38 3837
13. Kopell N and Landman M J 1995 SIAM J. Appl. Math. 55 1297
14. Zakharov V E and Shvets V F 1988 JETP Lett. 47 275 Kosmatov N E, Shvets V F and Zakharov V E 1991 Phys. D 52 16 Vlasov S N, Piskunova L V and Talanov V I 1986 Sov. Phys. JETP 68 1125
15. Zakharov V E and Shvets V F 1988 JETP Lett. 47 275 Kosmatov N E, Shvets V F and Zakharov V E 1991 Phys. D 52 16 Vlasov S N, Piskunova L V and Talanov V I 1986 Sov. Phys. JETP 68 1125
16. Zakharov V E and Shvets V F 1988 JETP Lett. 47 275 Kosmatov N E, Shvets V F and Zakharov V E 1991 Phys. D 52 16 Vlasov S N, Piskunova L V and Talanov V I 1986 Sov. Phys. JETP 68 1125
17. Fibich G and Papanicolaou G 1999 SIAM J. Appl. Math. 60 183 Plechak P and Sverak V 2001 Commun. Pure Appl. Math. 54 1215 Budd C J 2001 SIAM J. Appl. Math. 62 801
18. Fibich G and Papanicolaou G 1999 SIAM J. Appl. Math. 60 183 Plechak P and Sverak V 2001 Commun. Pure Appl. Math. 54 1215 Budd C J 2001 SIAM J. Appl. Math. 62 801
19. Fibich G and Papanicolaou G 1999 SIAM J. Appl. Math. 60 183 Plechak P and Sverak V 2001 Commun. Pure Appl. Math. 54 1215 Budd C J 2001 SIAM J. Appl. Math. 62 801
20. Aronson D G, Betelu S I and Kevrekidis I G 2001 nlin.AO/0111055
21. Weinstein M I 1999 Nonlinearity 12 673 Malomed B A and Weinstein M I 1996 Phys. Lett. A 220 91 Flach S, Kladko K and MacKay R S 1997 Phys. Rev. Lett. 78 1207
22. Weinstein M I 1999 Nonlinearity 12 673 Malomed B A and Weinstein M I 1996 Phys. Lett. A 220 91 Flach S, Kladko K and MacKay R S 1997 Phys. Rev. Lett. 78 1207
23. Weinstein M I 1999 Nonlinearity 12 673 Malomed B A and Weinstein M I 1996 Phys. Lett. A 220 91 Flach S, Kladko K and MacKay R S 1997 Phys. Rev. Lett. 78 1207
24. Ablowitz M J and Segur H 1981 Solitons and the Inverse Scattering Transform (Philadelphia, PA: SIAM)
25. Landman M J, Papanicolaou G C, Sulem C, Sulem P L and Wang X P 1991 Physica D 47 393
26. Ren W and Wang X P 2000 J. Comput. Phys. 159 246
27. Rowley C W and Marsden J E 2000 Physica D 142 1 Rowley C W, Kevrekidis I G, Marsden J E and Lust K 2002 Nonlinearity submitted
28. Rowley C W and Marsden J E 2000 Physica D 142 1 Rowley C W, Kevrekidis I G, Marsden J E and Lust K 2002 Nonlinearity submitted
29. Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103 Zakharov V E 1968 Sov. Phys. JETP 26 994 Vakhitov N G and Kolokolov A A 1973 Radiophys. Quantum Electron. 16 783 Laedke E W, Spatschek K H and Stenflo L 1983 J. Math. Phys. 24 2764
30. Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103 Zakharov V E 1968 Sov. Phys. JETP 26 994 Vakhitov N G and Kolokolov A A 1973 Radiophys. Quantum Electron. 16 783 Laedke E W, Spatschek K H and Stenflo L 1983 J. Math. Phys. 24 2764
31. Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103 Zakharov V E 1968 Sov. Phys. JETP 26 994 Vakhitov N G and Kolokolov A A 1973 Radiophys. Quantum Electron. 16 783 Laedke E W, Spatschek K H and Stenflo L 1983 J. Math. Phys. 24 2764
32. Kuznetsov E A, Rubenchik A M and Zakharov V E 1986 Phys. Rep. 142 103 Zakharov V E 1968 Sov. Phys. JETP 26 994 Vakhitov N G and Kolokolov A A 1973 Radiophys. Quantum Electron. 16 783 Laedke E W, Spatschek K H and Stenflo L 1983 J. Math. Phys. 24 2764
33. Doedel E J 1991 Int. J. Bifurcat. Chaos 1 493
34. Kivshar Yu S and Malomed B A 1989 Rev. Mod. Phys. 61 763
35. Grillakis M, Shatah J and Strauss W 1987 J. Funct. Anal. 74 160 Grillakis M 1988 Commun. Pure Appl. Math. 41 745 Grillakis M 1988 J. Funct. Anal. 43 299
36. Grillakis M, Shatah J and Strauss W 1987 J. Funct. Anal. 74 160 Grillakis M 1988 Commun. Pure Appl. Math. 41 745 Grillakis M 1988 J. Funct. Anal. 43 299
37. Grillakis M, Shatah J and Strauss W 1987 J. Funct. Anal. 74 160 Grillakis M 1988 Commun. Pure Appl. Math. 41 745 Grillakis M 1988 J. Funct. Anal. 43 299
38. Pelinovsky D 1998 Physica D 119 301