Discrete compactons: Some exact results

Journal of Physics A: Mathematical and General

Volumn 35, Issue 45, 2002, Pages

  Kevrekidis, P G ^a,c   Konotop, V V ^b   Bishop, A R ^c   Takeno, S ^d  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b Centro de Fisica da Materia Condensada   (Portugal)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d NAGASAKI INSTITUTE OF APPLIED SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037111749     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/35/45/103     Document Type: Review

References (39)

1. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
2. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
3. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
4. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
5. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
6. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
7. Rosenau P and Hyman J M 1993 Phys. Rev. Lett. 70 564 Rosenau P 1994 Phys. Rev. Lett. 73 1737 Olver P J and Rosenau P 1996 Phys. Rev. E 53 1900 Rosenau P 1996 Phys. Lett. A 211 265 Rosenau P 1997 Phys. Lett. A 230 305 Rosenau P 1999 Phys. Lett. A 252 297 Rosenau P 2000 Phys. Lett. A 275 193
8. See, e.g., Dey B and Khare A 1998 Phys. Rev. E 58 R2741 Cooper F, Hyman J M and Khare A 2001 Phys. Rev. E 64 026608 Ismail M S and Al-Solamy F R 2001 Int. J. Comput. Math. 76 549 Gisiger T and Paranjape M B 1997 Phys. Rev. D 55 7731
9. See, e.g., Dey B and Khare A 1998 Phys. Rev. E 58 R2741 Cooper F, Hyman J M and Khare A 2001 Phys. Rev. E 64 026608 Ismail M S and Al-Solamy F R 2001 Int. J. Comput. Math. 76 549 Gisiger T and Paranjape M B 1997 Phys. Rev. D 55 7731
10. See, e.g., Dey B and Khare A 1998 Phys. Rev. E 58 R2741 Cooper F, Hyman J M and Khare A 2001 Phys. Rev. E 64 026608 Ismail M S and Al-Solamy F R 2001 Int. J. Comput. Math. 76 549 Gisiger T and Paranjape M B 1997 Phys. Rev. D 55 7731
11. See, e.g., Dey B and Khare A 1998 Phys. Rev. E 58 R2741 Cooper F, Hyman J M and Khare A 2001 Phys. Rev. E 64 026608 Ismail M S and Al-Solamy F R 2001 Int. J. Comput. Math. 76 549 Gisiger T and Paranjape M B 1997 Phys. Rev. D 55 7731
12. Dodd R K, Eilbeck J C, Gibbon J D and Morris H C 1982 Solitons and Nonlinear Wave Equations (London: Academic)
13. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
14. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
15. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
16. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
17. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
18. Aubry S 1997 Physica D 103 201 Braun O M and Kivshar Yu S 1998 Phys. Rep. 306 2 Flach S and Willis C R 1998 Phys. Rep. 295 181 Flach S and Willis C R 1998 Physica D 119 (special volume edited by S Flach and R S MacKay) Hennig D and Tsironis G P 1999 Phys. Rep. 307 334 Kevrekidis P G, Rasmussen K Ø and Bishop A R 2001 Int. J. Mod. Phys. B 15 2833
19. Konotop V V and Takeno S 1996 Phys. Rev. E 54 2010 Konotop V V and Takeno S 1996 Phys. Rev. E 60 1001
20. Konotop V V and Takeno S 1996 Phys. Rev. E 54 2010 Konotop V V and Takeno S 1996 Phys. Rev. E 60 1001
21. Kevrekidis P G and Konotop V V 2002 Phys. Rev. E 65 066614
22. Dinda P T and Remoissenet M 1999 Phys. Rev. E 60 6218 Coquet E, Remoissenet M and Dinda P T 2000 Phys. Rev. E 62 5767 Eleftheriou M, Dey B and Tsironis G P 2000 Phys. Rev. E 62 7540 Dey B, Eleftheriou M, Flach S and Tsironis G P 2001 Phys. Rev. E 65 017601
23. Dinda P T and Remoissenet M 1999 Phys. Rev. E 60 6218 Coquet E, Remoissenet M and Dinda P T 2000 Phys. Rev. E 62 5767 Eleftheriou M, Dey B and Tsironis G P 2000 Phys. Rev. E 62 7540 Dey B, Eleftheriou M, Flach S and Tsironis G P 2001 Phys. Rev. E 65 017601
24. Dinda P T and Remoissenet M 1999 Phys. Rev. E 60 6218 Coquet E, Remoissenet M and Dinda P T 2000 Phys. Rev. E 62 5767 Eleftheriou M, Dey B and Tsironis G P 2000 Phys. Rev. E 62 7540 Dey B, Eleftheriou M, Flach S and Tsironis G P 2001 Phys. Rev. E 65 017601
25. Dinda P T and Remoissenet M 1999 Phys. Rev. E 60 6218 Coquet E, Remoissenet M and Dinda P T 2000 Phys. Rev. E 62 5767 Eleftheriou M, Dey B and Tsironis G P 2000 Phys. Rev. E 62 7540 Dey B, Eleftheriou M, Flach S and Tsironis G P 2001 Phys. Rev. E 65 017601
26. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
27. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
28. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
29. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
30. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
31. Jensen M H, Bak P and Popielewicz A 1983 J. Phys. A: Math. Gen. 16 4369 Bressloff P C and Rowlands G 1997 Physica D 106 255 Flach S, Zolotaryuk Y and Kladko K 1999 Phys. Rev. E 59 6105 Comte J C, Marquié P and Remoissenet M 1999 Phys. Rev. E 60 7487 Comte J C 2002 Phys. Rev. E 65 046619 Comte J C 2002 Phys. Rev. E 65 067601
32. Schmidt V H 1979 Phys. Rev. B 20 4397
33. Ablowitz M J and Ladik J F 1975 J. Math. Phys. 16 598 Ablowitz M J and Ladik J F 1976 J. Math. Phys. 17 1011
34. Ablowitz M J and Ladik J F 1975 J. Math. Phys. 16 598 Ablowitz M J and Ladik J F 1976 J. Math. Phys. 17 1011
35. Laedke E W, Kluth O and Spatschek K H 1996 Phys. Rev. E 54 4299 Darmanyan S, Kobyakov A and Lederer F 1998 Sov. Phys.-JETP 86 682 Kevrekidis P G, Bishop A R and Rasmussen K Ø 2001 Phys. Rev. E 63 036603 Kapitula T, Kevrekidis P G and Malomed B 2001 Phys. Rev. E 63 036604 Kevrekidis P G 2001 Phys. Rev. E 64 026611
36. Laedke E W, Kluth O and Spatschek K H 1996 Phys. Rev. E 54 4299 Darmanyan S, Kobyakov A and Lederer F 1998 Sov. Phys.-JETP 86 682 Kevrekidis P G, Bishop A R and Rasmussen K Ø 2001 Phys. Rev. E 63 036603 Kapitula T, Kevrekidis P G and Malomed B 2001 Phys. Rev. E 63 036604 Kevrekidis P G 2001 Phys. Rev. E 64 026611
37. Laedke E W, Kluth O and Spatschek K H 1996 Phys. Rev. E 54 4299 Darmanyan S, Kobyakov A and Lederer F 1998 Sov. Phys.-JETP 86 682 Kevrekidis P G, Bishop A R and Rasmussen K Ø 2001 Phys. Rev. E 63 036603 Kapitula T, Kevrekidis P G and Malomed B 2001 Phys. Rev. E 63 036604 Kevrekidis P G 2001 Phys. Rev. E 64 026611
38. Laedke E W, Kluth O and Spatschek K H 1996 Phys. Rev. E 54 4299 Darmanyan S, Kobyakov A and Lederer F 1998 Sov. Phys.-JETP 86 682 Kevrekidis P G, Bishop A R and Rasmussen K Ø 2001 Phys. Rev. E 63 036603 Kapitula T, Kevrekidis P G and Malomed B 2001 Phys. Rev. E 63 036604 Kevrekidis P G 2001 Phys. Rev. E 64 026611
39. Laedke E W, Kluth O and Spatschek K H 1996 Phys. Rev. E 54 4299 Darmanyan S, Kobyakov A and Lederer F 1998 Sov. Phys.-JETP 86 682 Kevrekidis P G, Bishop A R and Rasmussen K Ø 2001 Phys. Rev. E 63 036603 Kapitula T, Kevrekidis P G and Malomed B 2001 Phys. Rev. E 63 036604 Kevrekidis P G 2001 Phys. Rev. E 64 026611