Theory of optical dispersive shock waves in photorefractive media

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 5, 2007, Pages

  El, G A ^a   Gammal, A ^b   Khamis, E G ^b   Kraenkel, R A ^c   Kamchatnov, A M ^d  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^d INSTITUTE OF SPECTROSCOPY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; OPTICAL VARIABLES MEASUREMENT; PHOTOREFRACTIVE MATERIALS; REFRACTIVE INDEX;

CYLINDRICAL SYMMETRY; OPTICAL DISPERSIVE SHOCK WAVES; PHOTOREFRACTIVE MEDIA;

SHOCK WAVES;

EID: 36049031299     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.053813     Document Type: Article

References (40)

1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, Amsterdam, 2003).
2. W. Królikowski and B. Luther-Davies, IEEE J. Quantum Electron. IEJQA7 0018-9197 39, 3 (2003).
3. G. B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1974).
4. B. Benjamin and M. J. Lighthill, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 A224, 448 (1954).
5. M. Khan, S. Ghosh, S. Sarkar, and M. R. Gupta, Phys. Scr. PHSTBO 0031-8949 T116, 5356 (2005).
6. M. A. Hoefer, M. J. Ablowitz, I. Coddington, E. A. Cornell, P. Engels, and V. Schweikhard, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.023623 74, 023623 (2006).
7. A. M. Kamchatnov, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(96) 00049-X 286, 199 (1997).
8. V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, JETP JTPHES 1063-7761 111, 705 (1997).
9. Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. OPLEDP 0146-9592 15, 716 (1996).
10. Z. Chen, M. Segev, S. R. Singh, T. H. Coskun, and D. N. Christodoulides, J. Opt. Soc. Am. B JOBPDE 0740-3224 14, 1407 (1997).
11. G. Couton, H. Mailotte, and M. Chauvet, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/6/5/009 6, S223 (2004).
12. V. A. Brazhnyi and A. M. Kamchatnov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.043614 68, 043614 (2003).
13. W. Wan, S. Jia, and J. W. Fleischer, Nat. Phys. ZZZZZZ 1745-2473 3, 46 (2007).
14. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.043903 99, 043903 (2007).
15. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons, and Chaos, 2nd ed. (Cambridge University Press, Cambridge, England, 2000).
16. A. M. Kamchatnov, Nonlinear Periodic Waves and Their Modulations (Singapore, World Scientific, 2000).
17. M. G. Forest and J. Lee, in Oscillation Theory, Computation, and Methods of Compensed Compactness, edited by, C. Dafermos, (Springer, New York, 1986), Vol. 2, pp. 35-69.
18. M. V. Pavlov, Theor. Math. Phys. TMPHAH 0040-5779 10.1007/BF01017090 71, 584 (1987).
19. A. V. Gurevich and A. L. Krylov, JETP JTPHES 1063-7761 92, 1684 (1987).
20. G. A. El, V. V. Geogjaev, A. V. Gurevich, and A. L. Krylov, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95)00147-V 87, 186 (1995).
21. G. A. El and A. L. Krylov, Phys. Lett. A PYLAAG 0375-9601 203, 77 (1995).
22. S. Jin, C. D. Levermore, and D. W. McLaughlin, Commun. Pure Appl. Math. CPMAMV 0010-3640 10.1002/(SICI)1097-0312(199905)52:5<613::AID-CPA2>3.0. CO;2-L 52, 613 (1999).
23. F.-R. Tian and J. Ye, Commun. Pure Appl. Math. CPMAMV 0010-3640 10.1002/(SICI)1097-0312(199906)52:6<655::AID-CPA1>3.0.CO;2-A 52, 655 (1999).
24. A. M. Kamchatnov, R. A. Kraenkel, and B. A. Umarov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.036609 66, 036609 (2002).
25. G. Biondini and Y. Kodama, J. Nonlinear Sci. JNSCEK 0938-8794 16, 435 (2006).
26. Y. Kodama, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139997328155 59, 2162 (1999).
27. A. M. Kamchatnov, A. Gammal, and R. A. Kraenkel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.063605 69, 063605 (2004).
28. G. A. El, Chaos CHAOEH 1054-1500 10.1063/1.1947120 15, 037103 (2005).
29. A. V. Tyurina and G. A. El, JETP JTPHES 1063-7761 10.1134/1.558837 88, 615 (1999).
30. G. A. El, V. V. Khodorovskii, and A. V. Tyurina, Physica D PDNPDT 0167-2789 10.1016/j.physd.2005.05.010 206, 232 (2005).
31. G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74. 1978 74, 1978 (1995).
32. L. D. Landau, and E. M. Lifshitz, Fluid Mechanics (Pergamon, Oxford, 1987).
33. A. V. Gurevich and L. P. Pitaevskii, Sov. Phys. JETP SPHJAR 0038-5646 38, 291 (1974).
34. A. V. Gurevich and A. P. Meshcherkin, Sov. Phys. JETP SPHJAR 0038-5646 60, 732 (1984).
35. C. Hou, Y. Pei, Z. Zhou, and X. Sun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.053817 71, 053817 (2005).
36. R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley-Interscience, New York, 1962), Vol. II.
37. S. A. Darmanyan, A. M. Kamchatnov, and S. A. Neviére, JETP JTPHES 1063-7761 10.1134/1.1581941 96, 876 (2003).
38. R. Grimshaw, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 368, 359 (1979).
39. G. A. El, R. H. J. Grimshaw, and N. F. Smyth, nlin.PS/0710.3379 (2007).
40. G. A. El, R. H. J. Grimshaw, and N. F. Smyth, Phys. Fluids PHFLE6 1070-6631 10.1063/1.2175152 18, 027104 (2006).