Dissipative solitons with a Lagrangian approach

Optical Fiber Technology

Volumn 13, Issue 2, 2007, Pages 91-97

  Ankiewicz, Adrian ^a   Akhmediev, Nail ^a   Devine, Natasha ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Dissipative solitons; Fiber lasers; Lagrangian approach

Indexed keywords

APPROXIMATION THEORY; COMMUNICATION CHANNELS (INFORMATION THEORY); FIBER LASERS; LAGRANGE MULTIPLIERS; LASER MODE LOCKING; LIGHT TRANSMISSION;

COMPLEX GINZBURG-LANDAU EQUATION (CGLE); DISSIPATIVE SOLITONS; LAGRANGIAN APPROACH; PULSATING SOLITONS;

SOLITONS;

EID: 33947102214     PISSN: 10685200     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.yofte.2006.12.001     Document Type: Article

References (25)

1. Akhmediev N., and Ankiewicz A. Dissipative solitons in the complex Ginzburg-Landau and Swift-Hohenberg equations. In: Akhmediev N., and Ankiewicz A. (Eds). Dissipative Solitons (2005), Springer, Heidelberg
2. Akhmediev N., Soto-Crespo J.M., Grapinet M., and Grelu Ph. Dissipative soliton interactions inside a fiber laser cavity. Opt. Fiber Technol. 11 (2005) 209
3. Kutz J.N. Mode-locking of fiber lasers via nonlinear mode coupling. In: Akhmediev N., and Ankiewicz A. (Eds). Dissipative Solitons (2005), Springer, Heidelberg
4. Peschel U., Michaelis D., Bakonyi Z., Onishchukov G., and Lederer F. Dynamics of dissipative temporal solitons. In: Akhmediev N., and Ankiewicz A. (Eds). Dissipative Solitons (2005), Springer, Heidelberg
5. Ablowitz M.J., and Clarkson P.A. Solitons, Nonlinear Evolution Equations and Inverse Scattering. London Mathematical Society Lecture Notes Series vol. 149 (1991), Cambridge Univ. Press, Cambridge
6. Zabusky N.J., and Kruskal M.D. Interaction of 'solitons' in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 15 (1965) 240-243
7. Agrawal G.P. Nonlinear Fiber Optics. second ed. (1995), Academic Press, San Diego, CA
8. Faddeev L.D., and Takhtajan L.A. Hamiltonian Methods in the Theory of Solitons (1987), Springer, Berlin
9. Akhmediev N., Ankiewicz A., and Grimshaw R. Hamiltonian versus energy diagrams in soliton theory. Phys. Rev. E 59 5 (1999) 6088-6096
10. In: Akhmediev N., and Ankiewicz A. (Eds). Dissipative Solitons (2005), Springer, Heidelberg
11. Aronson I.S., and Kramer L. The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74 (2002) 99
12. Ippen E.P. Principles of passive mode locking. Appl. Phys. B 58 (1994) 159
13. Bakonyi Z., et al. Dissipative solitons and their critical slowing down near a supercritical bifurcation. J. Opt. Soc. Am. B 19 (2002) 487
14. Akhmediev N., and Ankiewicz A. Solitons: Nonlinear Pulses and Beams (1997), Chapman & Hall, London
15. Morse P.M., and Feshbach H. Methods of Theoretical Physics (1953), McGraw-Hill
16. Bonderson A.D., Lisak M., and Anderson D. Soliton perturbations: A variational principle for the soliton parameters. Phys. Scripta 20 (1979) 479
17. Ankiewicz A., Akhmediev N., Peng G.D., and Chu P.L. Limitations of the variational approach for soliton propagation in nonlinear couplers. Opt. Comm. 103 (1993) 410-416
18. Peng G.D., Chu P.L., and Ankiewicz A. Soliton propagation in saturable nonlinear fibre couplers. Int. J. Nonlinear Opt. Phys. 3 (1994) 69-87
19. Boardman A.D., and Velasco L. Gyroelectric cubic-quintic dissipative solitons. IEEE J. Select. Top. Quantum Electron. 12 (2006) 388
20. Manousakis M., et al. Propagation of chirped solitary pulses in optical transmission lines: Perturbed variational approach. Opt. Comm. 213 (2002) 293-299
21. Chavez Cerda S., et al. A variational approach of nonlinear dissipative pulse propagation. Eur. J. Phys. D 1 (1998) 313-316
22. Tsoy E., Ankiewicz A., and Akhmediev N. Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation. Phys. Rev. E 73 (2006) 036621
23. Akhmediev N.N., and Afanasjev V.V. Novel arbitrary-amplitude soliton solutions of the cubic-quintic complex Ginzburg-Landau equation. Phys. Rev. Lett. 75 12 (1995) 2320-2323
24. Akhmediev N., Soto-Crespo J.M., and Town G. Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg-Landau equation. Phys. Rev. E 63 (2001) 056602
25. Anderson D. Variational approach to nonlinear pulse propagation in optical fibers. Phys. Rev. A 27 6 (1983) 3135-3145