Solitons and symmetries

Journal of Engineering Mathematics

Volumn 36, Issue 1-2, 1999, Pages 1-91

  Ablowitz, M J ^a,b   Clarkson, P A ^a  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Fibre optics; Review; Solitons; Symmetries

Indexed keywords

FIBER OPTICS; NONLINEAR EQUATIONS; PROBLEM SOLVING; WAVES;

SOLITARY WAVE; SYMMETRIES;

SOLITONS;

FIBER OPTICS;

EID: 0033371590     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004581620608     Document Type: Article

References (57)

1. J. Scott Russell, Report of the Committee on Waves. (1838) Report of the 7th Meeting of the British Association for the Advancement of Science, Liverpool 411-496.
2. ]. Scott Russell, Report on Waves. Report of the 14th Meeting of the British Association forthe Advancement of Science. London: John Murray (1844) 311-390.
3. J. Boussinesq, Théorie de l'intumescence appelée onde solitaire ou de translation se propagente dans un canal rectangulaire. C.R. Acad. Se. Paris 72 (1871) 755-759.
4. J. Boussinesq, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenudans ce canal des vitesses sensiblemant pareilles de la surface au fond. J. Math. PureAppl. Ser. (2) 1 (1872) 55-108.
5. J. Boussinesq, Essai sur la théorie des eaux courants. Mein. Acad. Sci. Inst. Nat. France 23(1) (1877) 1-680.
6. D. J. Korteweg and G. de Vries, On thé change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. Mag. Ser. 5, 39 (1895) 422-443.
7. M. J. Ablowitz and P. A. Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering L.M.S. Lect. Note Series 149. Cambridge: C.U.P. (1991) 516 pp.
8. M. J. Ablowitz and H. Segur. Solitons and the Inverse Scattering Transform. Philadelphia: SIAM (1981) 425pp.
9. C. S. Gardner and G. K. Morikavva, Similarity in the asymptotic behaviour of collision free hydrodynamic waves and water waves. Courant Inst. Math. Sci. Res. Rep. NYO-9082, New York University, New York, (1960).
10. A. Fermi, J. Pasta and S. Ulum, Studies of nonlinear problems. I. Los Alamos Report LA1940. Reproduced in 'Nonlinear Wave Motion,' proceedings, Potsdam, New York, 1972, ed. A. C. Newell, Lect. Appl. Math., 15 (1955) 143-156, A.M.S., Providence, RI (1974).
11. N. J. Zabusky and M. D. Kruskal. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-243.
12. D. H. Peregrine, Calculations on the development of an undular bore. J. Fluid Mech. 25 (1966) 321-330.
13. T. B. Benjamin, J. L. Bona and J. J. Mahoney, Model equations for long waves in nonlinear dispersive systems. Phil. Trans. Roy. Soc. A272 (1972) 47-78.
14. K. O. Abdulloev, I. L. Bogolubsky and V. G. Makhankov, One more example of inelastic soliton interactions. Phys. Lett. A 56 (1976) 427-428. :
15. C. S. Gardner, J. M. Greene, M. D. Kruskal and R. M. Miura, Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967) 1095-1097.
16. V. E. Zakharov and L. D. Faddeev. Korteweg-de Vries equation, a completely integrable Hamiltonian System. Funct. Anal. Appl. 5 (1971) 280-287.
17. V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional of waves in nonlinear media. Sov. Phys. JETP 34 (1972) 62-69.
18. D. J. Benney and A. C. Newell, The propagation of nonlinear wave envelopes. J. Math. & Phys. (Stud. Appl. Math.) 46 (1967) 133-139.
19. D. J. Benney and G. J. Roskes. Waves instabilities. Stud. Appl. Math. 48 (1969) 377-385.
20. V. E. Zakharov, Stability of periodic waves of finite amplitude on the surface of a deep fluid. Sov. Phys. J. Appl. Mech. Tech. Phys. 4 (1968) 190-194.
21. A. Hasegawa and F. D. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibres. I. Anomalous dispersion. Appl. Phys. Lett. 23 (1973) 142-144.
22. A. Hasegawa and F. D. Tappert, Transmission of stationary nonlinear optical pulses in dispersive dielectric fibres. II. Normal dispersion. Appl. Phys. Lett. 23 (1973) 171-172.
23. L. F. Mollenauer and R. H. Stolen, Solitons in optical fibres. Laser Focus 18 (1982) 193-198.
24. L. F. Mollenauer, R. H. Stolen and J. P. Gordon. Experimental observation of picosecond pulse narrowing and solitons in optical fibres. Phys. Rev. Lett. 45 (1983) 1045-1048.
25. L. F. Mollenauer, Solitons in optical fibres and the soliton laser. Phil. Trans. Roy. Soc. London A 315A (1985) 437-450.
26. E. Desurvire, J. R. Simpson and P. C. Beeker, High-gain Erbium-doped traveling-wave fibre amplifier Opt. Lett. 12 (1987) 888-890.
27. R. J. Mears, L. Reekie, I. M. Janucey and D. N. Payne, Low-noise Erbium-doped fibre amplifier operating at 1.54 fim. Electron. Lett. 23 (1987) 1026-1028.
28. A. Hasegawa and Y. Kodama, Solitons in Optical Communications. Oxford: O.U.P. (1995) 320 pp.
29. Y. Kodama and A. Hasegawa, Nonlinear puise propagation in a monomode dielectric guide, IEEE J. Quantum Electron. 23 (1987) 510-524.
30. J. P. Gordon and H. A. Haus, Random walk of coherently amplified solitons in optical fibre transmission. Opt. Lett. 11 (1986) 665-667.
31. Y. Kodama and A. Hasegawa, Generation of asymptotically stable optical solitons and suppression of the Gordon-Haus effect. Opt. Lett. 17 (1992) 31-33.
32. A. Mecozzi, J. D. Moores, H. A. Haus and Y. Lai, Soliton transmission control Opt. Lett. 16 (1991) 1841-1843.
33. L. F. Mollenauer, E. Lichtman, M. J. Neubelt and G. T. Harvey, Demonstration, using sliding-frequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10Gbit/s, single channel, and over more than 13 Mm at 20 Gbit/s in a two channel WDM. Electron. Lett. 29 (1993) 910-911.
34. M. J. Ablowitz, G. Biondini, S. Chakravarty, R. B. Jenkins and J. R. Sauer, Four-wave mixing in wavelengthdivision multiplexed soliton systems-damping and amplification. Opt. Lett. 21 (1996) 1646-1648.
35. P. V. Mamyshev and L. F. Mollenauer, Pseudo-phase-matched four-wave mixing in soliton wavelengthdivision multiplexing transmission. Opt. Lett. 21 (1996) 396-398.
36. M. J. Ablowitz, G. Biondini, R. Home and S. Chakravarty, On timing jitter in svavelength-division multiplexed soliton systems. Optics Commun. 150 (1998) 305-318.
37. A. Mecozzi, Timing jitter inwavelength-division multiplexed filtered soliton transmission. J. Opt Soc Amer B 13 (1998) 152-161.
38. L. F. Mollenauer, S. G.' Evangelides and J. P. Gordon, Wavelength division multiplexing with solitons in ultra-long distance transmission using lumped amplifiers. J. Lighhvave Teclinol. 9 (1991) 362-367.
39. N. J. Smith, N. J. Doran, F. M. Knox and W. Forysiak, Energy-scaling characteristics of solitons in strongly dispersion-managed fibers. Opt. Lett. 21 (1996) 1981-1983.
40. J. F. L. Devaney, W. Forysiak, A. M. Niculae and N. J. Doran, Soliton collisions in dispersion-managed wavelength-division-multiplexed systems. Opt. Lett. 22 (1997) 1695-1697.
41. J. H. B. Nijhof, N. J. Doran, W. Forysiak and F. M. Knox, Stable soliton-like propagation in dispersionmanaged systems with net anomalous, zero and normal dispersion. Electron. Lett. 33 (1997) 1726-1727.
42. E. A. Golovchenko, A. N. Pilipetskii and C. R. Menyuk, Periodic dispersion management in soliton wavelength-division-multiplexing transmission with strong filters. Opt. Lett. 22 (1997) 1156-1158.
43. V. S. Grigoryan, T. Yu, E. A. Golovchenko, C. R. Menyuk and A. N. Pilipetskii, Dispersion-managed soliton dynamics. Opt. Lett. 22 (1997) 1609-1611.
44. E. A. Golovchenko, A. N. Pilipetskii and C. R. Menyuk, Collision-induced timing jitter reduction by periodic dispersion management in soliton WDM transmission. Elect. Lett. 3 (1997) 735-737.
45. V. S. Grigoryan and C. R. Menyuk, Dispersion-managed solitons at normal average dispersion. Opt. Lett. 23 (1998)609-611.
46. J. N. Kutz and S. G. Evangelides, Dispersion-managed breathers with average normal dispersion. Opt. Lett. 2(1998)685-687.
47. S. K. Turitsyn, Theory of average pulse propagation in high-bit-rate optical transmission systems with strong dispersion management. Sov. Phys. JETP Lett. 65 (1997) 845-851.
48. I. R. Gabitov and S. K. Turitsyn. Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation. Opt. Lett. 21 (1996) 327-329.
49. I. R. Gabitov, E. G. Shapiro and S. K. Turitsyn, Optical pulse dynamics in fiber links with dispersion compensation. Opt. Commun. 134 (1997) 317-329.
50. S. K. Turitsyn and E. G. Shapiro, Dispersion-managed solitons in optical amplifier transmission systems with zero average dispersion. Opt. Lett. 2 (1998) 682-684.
51. M. Suzuki, I. Morita, N. Edgawa, S. Yamamoto, H. Taga and S. Akiba, Reduction of Gordon-Haus timing jitter by periodic dispersion compensation in soliton transmission. Electron. Lett. 31 (1995) 2027-2029.
52. A. Hasegawa and Y. Kodama, Guiding-center soliton in optical fibers. Opt. Lett. 15 (1990) 1443-1445.
53. T.-S. Yang and W. L. Kath, Analysis of enhanced-power solitons in dispersion-managed optical fibers. Opt. Lett. 22 (1997) 985-987.
54. M. J. Ablowitz and G. Biondini, Multiscale pulse dynamics in communication systems with strong dispersion management. Opt. Lett. 23 (1998) 1668-1670.
55. F. Abdullaev, S. Darmanyan and P. Khabibullaev, Optical Solitons. Berlin: Springer-Verlag (1993).
56. N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams. London: Chapman & Hall (1997) 336pp.
57. A. C. Newell and J. J. Moloney, Nonlinear Optics. Redwood City, CA: Addison Wesley (1992) 436pp.