Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schrödinger equations

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

Volumn 75, Issue 3, 2007, Pages

  Zhu, Yi ^a   Yang, Jianke ^b  

^a TSINGHUA UNIVERSITY   (China)

^b University of Vermont   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTALS; INTEGRAL EQUATIONS; SCHRODINGER EQUATION; WAVE EQUATIONS;

FRACTAL STRUCTURES; INTEGRABLE DYNAMICAL EQUATIONS; SATURABLE NONLINEARITY; WEAK INTERACTIONS;

SOLITONS;

EID: 33947181965     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.036605     Document Type: Article

References (39)

1. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, Philadelphia, 1981).
2. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
3. W. Krolikowski, B. Luther-Davies, C. Denz, and T. Tschudi, Opt. Lett. OPLEDP 0146-9592 23, 97 (1998).
4. C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.2332 83, 2332 (1999).
5. Z. Chen, M. Acks, E. A. Ostrovskaya, and Y. S. Kivshar, Opt. Lett. OPLEDP 0146-9592 25, 417 (2000).
6. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
7. T. Dohnal and A. B. Aceves, Stud. Appl. Math. SAPMB6 0022-2526 10.1111/j.1467-9590.2005.00326.x 115, 209 (2005).
8. S. P. Yukon and N. C. H. Lin, IEEE Trans. Magn. IEMGAQ 0018-9464 10.1109/20.133778 27, 2736 (1991).
9. V. I. Karpman and V. V. Solov'ev, Physica D PDNPDT 0167-2789 10.1016/0167-2789(81)90123-8 3, 142 (1981).
10. V. S. Gerdjikov, D. J. Kaup, I. M. Uzunov, and E. G. Evstatiev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3943 77, 3943 (1996).
11. V. S. Gerdjikov, E. V. Doktorov, and J. Yang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056617 64, 056617 (2001).
12. J. Yang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036606 65, 036606 (2002).
13. M. J. Ablowitz, M. D. Kruskal, and J. F. Ladik, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0136033 36, 428 (1979).
14. D. K. Campbell, J. S. Schonfeld, and C. A. Wingate, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90289-0 9, 1 (1983).
15. M. Peyrard and D. K. Campbell, Physica D PDNPDT 0167-2789 10.1016/0167-2789(96)00086-3 9, 33 (1983).
16. D. K. Campbell and M. Peyrard, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90161-2 18, 47 (1986).
17. D. K. Campbell, M. Peyrard, and P. Sodano, Physica D PDNPDT 0167-2789 10.1016/0167-2789(86)90019-9 19, 165 (1986).
18. P. Anninos, S. Oliveira, and R. A. Matzner, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.44.1147 44, 1147 (1991).
19. T. I. Belova and A. E. Kudryavtsev, Phys. Usp. PHUSEY 1063-7869 10.1070/PU1997v040n04ABEH000227 40, 359 (1997).
20. Y. S. Kivshar, Fei Zhang, and L. Vázquez, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.1177 67, 1177 (1991).
21. Fei Zhang, Y. S. Kivshar, and L. Váquez, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.45.6019 45, 6019 (1992).
22. Z. Fei, Y. S. Kivshar, and L. Váquez, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.5214 46, 5214 (1992).
23. J. Yang and Y. Tan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3624 85, 3624 (2000).
24. J. Yang and Y. Tan, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01) 00040-8 280, 129 (2001).
25. Y. Tan and J. Yang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64. 056616 64, 056616 (2001).
26. S. V. Dmitriev, Yu. S. Kivshar, and T. Shigenari, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.056613 64, 056613 (2001).
27. S. V. Dmitriev and T. Shigenari, Chaos CHAOEH 1054-1500 10.1063/1.1476951 12, 324 (2002).
28. R. H. Goodman and R. Haberman, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.04.002 195, 303 (2004).
29. R. H. Goodman and R. Haberman, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.056605 71, 056605 (2005).
30. R. H. Goodman and R. Haberman, SIAM J. Appl. Dyn. Syst. ZZZZZZ 1536-0040 4, 1195 (2005).
31. T. Ueda and W. L. Kath, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.42.563 42, 563 (1990).
32. A. S. Kovalev and A. M. Kosevich, Fiz. Nizk. Temp. FNTEDK 0132-6414 2, 913 (1976).
33. N. G. Vakhitov and A. A. Kolokolov, Izv. Vyssh. Uchebn. Zaved., Radiofiz. IVYRAY 0021-3462 16, 1020 (1973)
34. N. G. Vakhitov and A. A. Kolokolov, [Radiophys. Quantum Electron. RPQEAC 0033-8443 10.1007/BF01031343 16, 783 (1973)].
35. I. V. Barashenkov and V. G. Makhankov, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(88)91042-0 128, 52 (1988).
36. K. A. Gorshkov and L. A. Ostrovsky, Physica D PDNPDT 0167-2789 10.1016/0167-2789(81)90146-9 3, 428 (1981).
37. J. Yang, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.026607 64, 026607 (2001).
38. J. Yang, and D. J. Kaup, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139998341898 60, 967 (2000).
39. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.046602 66, 046602 (2002).