Comparative study of different discretizations of the 4 model

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 2, 2007, Pages

  Roy, Ishani ^a,b,d   Dmitriev, Sergey V ^c,e   Kevrekidis, Panayotis G ^a   Saxena, Avadh ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b CENTER FOR NONLINEAR STUDIES   (United States)

^c INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

^d BROWN UNIVERSITY   (United States)

^e ALTAI STATE TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

SOLITONS; STATISTICAL MECHANICS;

4 FIELD THEORY; CONTINUUM LIMIT; LATTICE SPACING;

MATHEMATICAL MODELS;

EID: 34547670421     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.026601     Document Type: Article

References (45)

1. V. V. Konotop and V. A. Brazhnyi, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984904007190 18, 627 (2004);
2. P. G. Kevrekidis and D. J. Frantzeskakis, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984904006809 18, 173 (2004).
3. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature (London) NATUAS 0028-0836 10.1038/nature01936 424, 817 (2003);
4. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
5. M. Peyrard, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/2/R01 17, R1 (2004).
6. A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.60.781 60, 781 (1988).
7. V. K. Wadhawan, Introduction to Ferroic Materials (Gordon and Breach, Amsterdam, 2000).
8. W. Atkinson and N. Cabrera, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.138.A763 138, A763 (1965).
9. O. M. Braun and Y. S. Kivshar, The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Springer, Berlin, 2004).
10. Chaos CHAOEH 1054-1500 10.1063/1.1889345 15 (1) (2005), Focus issue: "The Fermi-Pasta-Ulam Problem-The First Fifty Years."
11. T. I. Belova and A. E. Kudryavtsev, Usp. Fiz. Nauk UFNAAG 0042-1294 167, 377 (1997)
12. [T. I. Belova and A. E. Kudryavtsev, Phys. Usp. PHUSEY 1063-7869 10.1070/PU1997v040n04ABEH000227 40, 359 (1997)].
13. P. Anninos, S. Oliveira, and R. A. Matzner, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.44.1147 44, 1147 (1991).
14. D. K. Campbell, J. F. Schonfeld, and C. A. Wingate, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90289-0 9, 1 (1983).
15. D. K. Campbell and M. Peyrard, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90161-2 18, 47 (1986);
16. D. K. Campbell and M. Peyrard, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90019-9 19, 165 (1986).
17. R. H. Goodman and R. Haberman, SIAM J. Appl. Dyn. Syst. SJADAY 1536-0040 4, 1195 (2005).
18. C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation (Springer-Verlag, New York, 1999).
19. J. M. Speight, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/12/5/311 12, 1373 (1999).
20. J. M. Speight and R. S. Ward, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/7/2/009 7, 475 (1994).
21. J. M. Speight, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/10/6/010 10, 1615 (1997).
22. E. B. Bogomol'nyi, Yad. Fiz. IDFZA7 0044-0027 24, 861 (1976)
23. [E. B. Bogomol'nyi, Sov. J. Nucl. Phys. SJNCAS 0038-5506 24, 449 (1976)].
24. J. M. Speight and Y. Zolotaryuk, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/19/6/008 19, 1365 (2006).
25. P. G. Kevrekidis, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(03)00153- 2 183, 68 (2003).
26. F. Cooper, A. Khare, B. Mihaila, and A. Saxena, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.036605 72, 036605 (2005).
27. S. V. Dmitriev, P. G. Kevrekidis, and N. Yoshikawa, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/35/002 38, 7617 (2005).
28. S. V. Dmitriev, P. G. Kevrekidis, N. Yoshikawa, and D. J. Frantzeskakis, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.046609 74, 046609 (2006).
29. I. V. Barashenkov, O. F. Oxtoby, and D. E. Pelinovsky, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.035602 72, 035602 (R) (2005);
30. O. F. Oxtoby, D. E. Pelinovsky, and I. V. Barashenkov, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/19/1/011 19, 217 (2006).
31. S. V. Dmitriev, P. G. Kevrekidis, A. A. Sukhorukov, N. Yoshikawa, and S. Takeno, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2006.03.056 356, 324 (2006);
32. P. G. Kevrekidis, S. V. Dmitriev, and A. A. Sukhorukov, Math. Comput. Simul. MCSIDR 0378-4754 74, 343 (2007).
33. D. E. Pelinovsky, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/19/11/ 010 19, 2695 (2006).
34. A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/4/002 38, 807 (2005);
35. A. Khare, K. Ø. Rasmussen, M. Salerno, M. R. Samuelsen, and A. Saxena, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.74.016607 74, 016607 (2006).
36. A. B. Adib and C. A. S. Almeida, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.037701 64, 037701 (2001).
37. M. J. Ablowitz and J. F. Ladik, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.522558 16, 598 (1975);
38. M. J. Ablowitz and J. F. Ladik, M. J. Ablowitz and J. F. Ladik, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523009 17, 1011 (1976).
39. P. G. Kevrekidis, C. K. R. T. Jones, and T. Kapitula, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00247-4 269, 120 (2000).
40. T. Sugiyama, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.61.1550 61, 1550 (1978).
41. B. I. Swanson, J. A. Brozik, S. P. Love, G. F. Strouse, A. P. Shreve, A. R. Bishop, W. Z. Wang, and M. I. Salkola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3288 82, 3288 (1999).
42. M. Peyrard and M. D. Kruskal, Physica D PDNPDT 0167-2789 10.1016/0167-2789(84)90006-X 14, 88 (1984).
43. E. N. Pelinovsky and S. K. Shavratsky, Physica D PDNPDT 0167-2789 10.1016/0167-2789(81)90144-5 3, 410 (1981).
44. M. Sato, B. E. Hubbard, and A. J. Sievers, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.137 78, 137 (2006).
45. J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.093903 93, 093903 (2004).