Exact analytical solutions to the nonlinear schrödinger equation model

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Volumn 2005, Issue , 2005, Pages 224-230

  Li, Biao ^a,b   Chen, Yong ^a,b   Wang, Qi ^b,c  

^a NINGBO UNIVERSITY   (China)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^c DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Nonlinear Schr dinger Equation; Soliton; Soliton Propagation and Interaction; Symbolic Computation

Indexed keywords

ABSORPTION; ASYMPTOTIC STABILITY; COMPUTATION THEORY; FUNCTIONS; PROBLEM SOLVING; SOLITONS;

ANALYTICAL SOLUTIONS; NONLINEAR SCHRÖDINGER EQUATION (NLSE); SOLITON PROPAGATION AND INTERACTION; SYMBOLIC COMPUTATION;

NONLINEAR EQUATIONS;

EID: 33749632312     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1073884.1073916     Document Type: Conference Paper

References (37)

1. M. Ablowitz and P. Clarkson. Soliton, Nonlinear-Evolution Equations and Inverse scattering. Cambridge University Press, Cambridge, England, 1991.
2. A. Arai. Exactly solvable supersymmetric quantum mechanics. J. Math. Anal. Appl. 158(1):63-79, 1991.
3. A. Arai. Exact solutions of multi-component nonlinear Schrödinger and Kleiri-Gordon equations in two-dimensional space-time. J. Phys. A, 34(20):4281-4288, 2001.
4. A. Bishop and T. Schneider. Solitons and Condensed Matter Physics. Springer-Verlag, New York, 1978.
5. R. Carnssa, J. Hyman, and B. Luce. Nonlinear waves and solitons in physical systems. Physics D, 123:1-20, 1998.
6. Y. Chen and B. Li. General projective Riccati equation method and exact solutions for generalized kdv-type and kdv-burgers-type equations with nonlinear terms of any order. Chaos, Solitons and Fractals, 19(4):977-984, May 2004.
7. R. Conte and M. Musette. Link between solitary waves and projective Riccati equations. J. Phys. A, 25(21):5609-5623, 1992.
8. E. Fan. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A, 277(4-5):212-218, December 2000.
9. E. Fan and Y. Hon. Applications of extended tanh method to special-types of nonlinear equations. Appl. Math. Comput., 141:351-358, 2003.
10. M. Gedalin, T. Scott, and Y. Band. Optical Solitary waves in the Higher-Order Nonlinear Schrödinger Equation. Phys. Rev. Lett., 78(3):448-451, 1996.
11. Y. Gao and B. Tian. Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics. Comput. Phys. Commun., 133(2-3): 158-164, January 2001.
12. A. Hasegawa. Quasi-soliton for ultra-high speed communications. Physics D, 123(1-4):267-270, November 1998.
13. A. Hasegawa and Y. Kodama. Solitons in Optical Communications. Oxford University Press, Oxford, 1995.
14. A. Hasegawa and F. Tapper. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. i. anomalous dispersion. Appl. Phys. Lett., 23:142-144, 1973.
15. J. Hong and Y. Liu, A novel numerical approach to simulating nonlinear Schrödinger equations with varying coefficients. Appl. Math. Lett., 16:759-765, 2003.
16. T. Inoue, H. Sugahara, A. Maruta, and Y. Kodama. Interactions between dispersion-managed solitons in optical-time-division-rnultiplexed systems. Electron. Commun. Japan, Part 2, 84(6):24-29, June 2001.
17. Y. S. Kivshar and B. Davies. Dark optical solitons: physics and applications. Phys. Rep., 298:81-197, 1998.
18. D. Kaup and A. Newell. The Goursat and Cauchy problems for the sine-Gordon equation. SIAM J. Appl. Math., 34(1):37-54, 1978.
19. S. Kumar and A. Hasegawa. Quasi-soliton propagation in dispersion-managed optical fibers. Opt. Lett., 22:372-374, 1997.
20. T. Lakoba and D. Kaup. Hermite-Gaussian expansion for pulse propagation in strongly dispersion managed fibers. Phys. Rev. E, 58:6728-6741, 1998.
21. B. Li and Y. Chen. Exact analytical solutions of the generalized Calogero-Bogoyavlenskii-Schiff equation using symbolic computation. Czechoslovak J. Phys., 54(5):517-528, 2004.
22. B. Li and Y. Chen. On exact solutions of the nonlinear schrodinger equations in optical fiber. Chaos, Solitons and Fractals, 21(1):241-247, 2004.
23. B. Li, Y. Chen, H. Xuan, and H. Zhang. Symbolic computation and construction of soliton-like solutions for a breaking soliton equation. Chaos, Solitons and Fractals, 17(5): 885-893, 2003.
24. B. Li, Y. Chen, and H. Zhang. Explicit exact solutions for new general two-dimensional kdv-type and two-dimensional kdv-burgers-type equations with nonlinear terms of any order. J. Phys. A, 35(39):8253-8265, 2002.
25. S. Lou, G. Huang, and H. Ruan. Exact solitary waves in a convecting fluid. J. Phys. A, 24:L587-L590, 1991.
26. W. Malfliet. Solitary wave solutions of nonlinear wave equations. Amer. J. Phys., 60(7):650-654, 1992.
27. L. Mollenaure, R. Stolen, and J. Gordon. Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett., 45:1095-1098, 1980.
28. E. Parkes and B. Duffy. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. Phys. Commun., 98(3):288-300, November 1996.
29. H. Ruan and Y. Chen. The study of exact solutions to the nonlinear Schrodinger equations in optical fiber. J. Phys. Soc. Jpn., 72(6):1350-1355, June 2003.
30. A. Scott, F. Chu, and D. McLaughlin. The soliton: a new concept in applied science. Proc. IEEE, 61:1443-1483, 1973.
31. V. Serkin and T. Belyaeva. Optimal compression of chirped solitary waves: importance of raman self-scattering effect and high-order dispersion. Proc. SPIE, 4271:280-291, 2001.
32. V. Serkin and A. Hasegawa. Femtosecond soliton amplification in nonlinear dispersive traps and soliton dispersion management. SPIE Proceedings, 3927, 2000.
33. V. Serkin and A. Hasegawa. Novel soliton solutions of the nonlinear Schrödinger equation model. Phys. Rev. Lett., 85:4502-4505, 2000.
34. Z. Xu, L. Li, Z. Li, G. Zhou, and K. Nakkeeran. Exact soliton solutions for the core of dispersion-managed solitons. Phys. Rev. E, 68:046605-(1-8), 2003.
35. Z. Yan. Generalized method and its application in the higher-order nonlinear Schrödinger equation in nonlinear optical fibres. Chaos, Solitons and Fractals, 16(5):759-766, June 2003.
36. Z. Yan New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations. Phys. Lett. A, 292(1-2):100-106, December 2001.
37. V. Zakharov and A. Shabat. Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP, 34(1):62-69, 1972.