Stability analysis for solitons in planar waveguides, fibres and couplers using Hamiltonian concepts

IEE Proceedings: Optoelectronics

Volumn 150, Issue 6, 2003, Pages 519-526

  Ankiewicz, A ^a   Akhmediev, N ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; HAMILTONIANS; LIGHT PROPAGATION; OPTICAL FIBERS; OPTICAL KERR EFFECT; REFRACTIVE INDEX; TIME DOMAIN ANALYSIS; WAVEGUIDE COUPLERS;

OPTICAL COUPLERS; SOLITON BEAMS;

SOLITONS;

EID: 0348167735     PISSN: 13502433     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-opt:20030609     Document Type: Article

References (21)

1. Goldstein, H.: 'Classical mechanics' (Addison-Wesley, New York, 1980, 2nd edn.)
2. Andronov, A., Vitt, A., and Khaikin, C.: 'Theory of oscillators' (Pergamon, Oxford, 1966)
3. Faddeev, L.D., and Takhtadjan, L.A.: 'Hamiltonian methods in the theory of solitons' (Springer-Verlag, Berlin, 1987)
4. Akhmediev, N.N., Ankiewicz, A., and Grimshaw, R.: 'Hamiltonian versus energy diagrams in soliton theory', Phys. Rev. E, Stat. Nonlinear Soft Matter Phys., 1999, 55, pp. 6088-6096
5. Kusmartsev, F.V.: 'Application of catastrophe theory to molecules and solitons', Phys. Rep., 1989, 183, pp. 1
6. Soto-Crespo, J.M., Akhmediev, N.N., and Ankiewicz, A.: 'Soliton propagation in optical devices with two-component fields: a comparative study', J. Opt. Soc. Am. B, Opt. Phys., 1995, 12, (6), pp. 1100-1109
7. Artigas, D., Torner, L., and Akhmediev, N.: 'Dynamics of quadratic soliton excitation', Opt. Commun., 1999, 162, pp. 347-356
8. Akhmediev, N.N., Das, M.P., and Vagov, A.: 'Bose-Einstein condensation of atoms with attractive interaction' Proc. 20th Int. Workshop on Condensed matter theories, 1997, Vol. 12, pp. 17-26
9. Jovanoski, Z., and Rowland, D.R.: 'Variational analysis of solitary waves in a homogeneous cubic-quintic nonlinear medium', J. Mod. Opt., 2001, 48, pp. 1179-1193
10. Biswas, A.: 'Perturbation of solitons with non-Kerr law nonlinearity', Chaos Solitons Fractals, 2002, 13, pp. 815-823
11. Akhmediev, N.N.: Sov. Phys.-JETP, 1982, 56, pp. 299-303
12. Mihalache, D., Bertolotti, M., and Sibilia, C.: 'Nonlinear wave propagation in planar structures', Prog. Opt., 1989, 27, pp. 229-313
13. Ankiewicz, A., and Tran, H.T.: 'A new class of nonlinear guided waves', J. Mod. Opt., 1991, 38, pp. 1093-1106
14. Akhmediev, N.N., and Ankiewicz, A.: 'Solitons: nonlinear pulses and beams' (Chapman & Hall, London, 1997)
15. Zakharov, V.E., and Rubenchik, A.M.: 'Instability of waveguides and solitons in nonlinear media', Sov. Phys.-JETP, 1973, 38, pp. 494
16. Grillakis, M., Shatah, J., and Strauss, W.: 'Stability theory of solitary waves in the presence of symmetry', J. Funct. Anal., 1987, 74, pp. 160-197
17. Tran, H.T., and Ankiewicz, A.: 'Instability regions of nonlinear planar guided waves', IEEE J. Quantum Electron., 1992, 28, pp. 488-492
18. Ankiewicz, A., and Akhmediev, N.N.: 'Analysis of bifurcations for parabolic nonlinearity optical couplers', Opt. Commun., 1996, 124, pp. 95-102
19. Torruellas, W., Wang, Z., and Menyuk, C.: 'Spatial solitary waves in a quadratic medium', Phys. Rev. Lett., 1995, 74, pp. 5036
20. Torruellas, W., Lawrence, B., and Stegeman, G.I.: 'Self-focusing and two-dimensional spatial solitons in PTS', Electron Lett., 1996, 32, pp. 2092
21. Ankiewicz, A., and Peng, G.D.: 'Accurate variational method for nonlinear fibre devices', Opt. Commun., 1991, 84, pp. 71-75