One- and two-dimensional solitons in second-harmonic-generating lattices

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

Volumn 65, Issue 5, 2002, Pages

  Malomed, Boris A ^a   Kevrekidis, P G ^b   Frantzeskakis, D J ^c   Nistazakis, H E ^c   Yannacopoulos, A N ^c  

^a TEL AVIV UNIVERSITY   (Israel)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

^c UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

HARMONIC INTERSITE COUPLINGS; INTRINSIC LOCALIZED MODES (ILM); JOSEPHSON LADDERS; NON-SITE QUADRATIC NONLINEARITY;

ANTIFERROMAGNETISM; APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATHEMATICAL MODELS; OPTICAL WAVEGUIDES; SECOND HARMONIC GENERATION;

SOLITONS;

EID: 41349088137     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.056606     Document Type: Article

References (46)

1. A. J. Sievers and S. Takeno, Phys. Rev. Lett. 61, 970 (1988).
2. J. B. Page, Phys. Rev. B 41, 7835 (1990).
3. S. Flach and C. R. Willis, Phys. Rep. 295, 181 (1998).
4. S. Aubry, Physica D 103, 201 (1997).
5. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Int. J. Mod. Phys. B 15, 2833 (2001).
6. U. T. Schwarz, L. Q. English, and A. J. Sievers, Phys. Rev. Lett. 83, 223 (1999).
7. B. L. 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. 82, 3288 (1999).
8. H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
9. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
10. E. Trias, J. J. Mazo, and T. P. Orlando, Phys. Rev. Lett. 84, 741 (2000).
11. P. Binder, D. Abraimov, A. V. Ustinov, S. Flach, and Y. Zolotaryuk, Phys. Rev. Lett. 84, 745 (2000).
12. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988); A. Aceves, C. De Angelis, S. Trillo, and S. Wabnitz, Ibid. 19, 332 (1994); A. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, ibid. 19, 1186 (1994); A. Aceves et al., Phys. Rev. Lett. 75, 73 (1995); A. Aceves and M. Santagiustina, Phys. Rev. E 56, 1113 (1997).
13. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988); A. Aceves, C. De Angelis, S. Trillo, and S. Wabnitz, Ibid. 19, 332 (1994); A. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, ibid. 19, 1186 (1994); A. Aceves et al., Phys. Rev. Lett. 75, 73 (1995); A. Aceves and M. Santagiustina, Phys. Rev. E 56, 1113 (1997).
14. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988); A. Aceves, C. De Angelis, S. Trillo, and S. Wabnitz, Ibid. 19, 332 (1994); A. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, ibid. 19, 1186 (1994); A. Aceves et al., Phys. Rev. Lett. 75, 73 (1995); A. Aceves and M. Santagiustina, Phys. Rev. E 56, 1113 (1997).
15. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988); A. Aceves, C. De Angelis, S. Trillo, and S. Wabnitz, Ibid. 19, 332 (1994); A. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, ibid. 19, 1186 (1994); A. Aceves et al., Phys. Rev. Lett. 75, 73 (1995); A. Aceves and M. Santagiustina, Phys. Rev. E 56, 1113 (1997).
16. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988); A. Aceves, C. De Angelis, S. Trillo, and S. Wabnitz, Ibid. 19, 332 (1994); A. Aceves, C. De Angelis, G. G. Luther, and A. M. Rubenchik, ibid. 19, 1186 (1994); A. Aceves et al., Phys. Rev. Lett. 75, 73 (1995); A. Aceves and M. Santagiustina, Phys. Rev. E 56, 1113 (1997).
17. A. Campa and A. Giansanti, Phys. Rev. E 58, 3585 (1998).
18. S. Darmanyan, A. Kobyakov, and F. Lederer, Phys. Rev. E 57, 2344 (1998).
19. C. Etrich, F. Lederer, B. A. Malomed, T. Peschel, and U. Peschel, Prog. Opt. 41, 483 (2000).
20. V. M. Agranovich, O. A. Dubovskii, and A. V. Orlov, Solid State Commun. 72, 491 (1989).
21. O. A. Dubovskii and A. V. Orlov, Phys. Solid State 41, 642 (1999); V. M. Agranovich, O. A. Dubovsky, A. M. Kamchatnov, and P. Reineker, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 355, 25 (2001).
22. O. A. Dubovskii and A. V. Orlov, Phys. Solid State 41, 642 (1999); V. M. Agranovich, O. A. Dubovsky, A. M. Kamchatnov, and P. Reineker, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 355, 25 (2001).
23. V. V. Konotop and B. A. Malomed, Phys. Rev. B 61, 8618 (2000).
24. O. Bang, P. L. Christiansen, and C. B. Clausen, Phys. Rev. E 56, 7257 (1997).
25. A. A. Sukhorukov, Yu. S. Kivshar, O. Bang, and C. M. Soukoulis, Phys. Rev. E 63, 016615 (2001).
26. See Ref. [4] and M. Johansson, S. Aubry, Yu. B. Gaididei, P. L. Christiansen, and K. Ø. Rasmussen, Physica D 119, 115 (1998).
27. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
28. D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
29. C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Yu. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
30. M. Johansson and S. Aubry, Phys. Rev. E 61, 5864 (2000).
31. P. G. Kevrekidis, K. Ø. Rasmussen, and A. R. Bishop, Math. Comput. Simul. 55, 449 (2001).
32. E. W. Laedke, O. Kluth, and K. H. Spatschek, Phys. Rev. E 54, 4299 (1996).
33. M. Johansson and S. Aubry, Nonlinearity 10, 1151 (1997).
34. S. Darmanyan, A. Kobyakov, and F. Lederer, JETP 86, 682 (1998).
35. P. G. Kevrekidis, A. R. Bishop, and K. Ø. Rasmussen, Phys. Rev. E 63, 036603 (2001).
36. J.-C. van der Meer, Nonlinearity 3, 1041 (1990); I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998); A. De Rossi, C. Conti, and S. Trillo, ibid. 81, 85 (1998).
37. J.-C. van der Meer, Nonlinearity 3, 1041 (1990); I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998); A. De Rossi, C. Conti, and S. Trillo, ibid. 81, 85 (1998).
38. J.-C. van der Meer, Nonlinearity 3, 1041 (1990); I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998); A. De Rossi, C. Conti, and S. Trillo, ibid. 81, 85 (1998).
39. P. G. Kevrekidis and T. Kapitula (unpublished).
40. M. Johansson and Yu. S. Kivshar, Phys. Rev. Lett. 82, 85 (1999).
41. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
42. V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
43. V. V. Steblina, Yu. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995); A. V. Buryak, Yu. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
44. C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse (Springer-Verlag, New York, 1999).
45. W. J. Firth and D. Skryabin, Phys. Rev. Lett. 79, 2450 (1997); D. V. Petrov and L. Tomer, Opt. Quantum Electron. 29, 1037 (1997).
46. W. J. Firth and D. Skryabin, Phys. Rev. Lett. 79, 2450 (1997); D. V. Petrov and L. Tomer, Opt. Quantum Electron. 29, 1037 (1997).