Soliton interactions in the vector NLS equation

Inverse Problems

Volumn 20, Issue 4, 2004, Pages 1217-1237

  Ablowitz, M J ^a   Prinari, B ^b   Trubatch, A D ^c  

^a UNIVERSITY OF COLORADO   (United States)

^b INFN SEZIONE DI LECCE   (Italy)

^c UNITED STATES MILITARY ACADEMY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; FIBER OPTICS; HAMILTONIANS; MATHEMATICAL MODELS; OPTICAL WAVEGUIDES; VECTORS; WAVE PROPAGATION;

INVERSE SCATTERING TRANSFORM (IST); KERR MEDIA; POLARIZATION SHIFT; SOLITON INTERACTIONS;

SOLITONS;

EID: 4043092771     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/20/4/012     Document Type: Article

References (27)

1. Manakov S 1974 On the theory of two-dimensional stationary self-focusing of electromagnetic waves Sov. Phys.-JETP 38 248
2. Menyuk C R 1987 Nonlinear pulse propagation in birefringent optical fibres IEEE J. Quantum Electron. 23 174-6
3. Evangelidis S G, Mollenauer L F, Gordon J P and Bergano N S 1992 Polarization multiplexing with solitons J. Lightwave Technol. 10 28-35
4. Marcuse D, Menyuk C R and Wai P K A 1997 Applications of the Manakov pmd equations to studies of signal propagation in fibres with randomly-varying birefringence J. Lightwave Technol. 15 1735-45
5. Makhan'kov V G and Pashaev O K 1992 Integrable pseudospin models in condensed matter Sov. Sci. Rev. Math. Phys. 9 1-152
6. Kang J U, Stegeman G I, Aitchison J S and Akhmediev N 1996 Phys. Rev. Lett. 76 3699
7. Radhakrishnan R, Lakshmanan M and Hietarinta J 1997 Inelastic collision and switching of coupled bright solitons in optical fibres Phys. Rev. E 56 2213
8. Anastassiou C, Segev M, Steiglitz K, Giordmaine J A, Mitchell M, Shih M, Lan S and Martin J 1999 Energy-exchange interactions between colliding vector solitons Phys. Rev. Lett. 83 2332
9. Jakubowsky M H, Steiglitz K and Squier R 1998 State transformations of colliding optical solitons and possible applications to computation in bulk media Phys. Rev. E 58 6752
10. Steiglitz K 2000 Time-gated Manakov solitons are computationally universal Phys. Rev. E 63 016608
11. Anastassiou C, Fleischer J W, Carmon T, Segev M and Steiglitz K 2001 Information transfer via cascaded collisions of vector solitons Opt. Lett. 26 1498
12. Ablowitz M J, Ohta Y and Trubatch A D 1999 On discretizations of the vector nonlinear Schrödinger equation Phys. Lett. A 253 287
13. Ablowitz M J, Prinari B and Trubatch A D 2003 Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge: Cambridge University Press)
14. Kanna T and Lakshmanan M 2001 Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations Phys. Rev. Lett. 86 5043
15. Kanna T and Lakshmanan M 2003 Exact soliton solutions of coupled nonlinear Schrödinger equations: shape changing collisions, logic gates and partially coherent solitons Preprint nlin.SI/0303025
16. Kulish P P 1976 Factorization of the classical and quantum S-matrix and conservation laws Theor. Math. Phys. 26 132-7
17. Tsuchida T, Ujino H and Wadati M 1999 J. Phys. A: Math. Gen. 32 2239
18. Tsuchida T 2003 N-soliton collision in the Manakov model Preprint nlin.SI/0302059
19. Borah A, Ghosh S and Nandy S 2002 Interaction of coupled higher order nonlinear Schrödinger equation solutions Eur. Phys. J. B 29 221-5
20. Park Q-H and Shin H J 2002 Systematic construction of vector solitons IEEE J. Sel. Top. Quantum Electron. 8 432-9
21. Drinfeld V G 1992 On some unsolved problems in quantum group theory Quantum Groups (Lecture Notes in Mathematics vol 1510) (Berlin: Springer) pp 1-8
22. Veselov A P 2002 Yang-Baxter maps and integrable dynamics Preprint math.QA/0205335
23. Goncharenko V M and Veselov A P 2003 Yang-Baxter maps and matrix solitons Preprint math-ph/0303032
24. Suris Y and Veseiov A P 2003 Lax matrices for Yang-Baxter maps Preprint math.QA/0304122
25. Soljačić M, Steiglitz K, Sears S M, Segev M, Jakubowski M H and Squier R 2003 Collisions of two solitons in an arbitrary number of coupled nonlinear Schrödinger equations Phys. Rev. Lett. 90 254102
26. Barad Y and Silberberg Y 1997 Phys. Rev. Lett. 78 3290
27. Cundiff S T et al 1999 Phys. Rev. Lett. 82 3988