×

Cnoidal and solitary wave solutions of the coupled higher order nonlinear Schrödinger equation in nonlinear optics. (English) Zbl 1138.35409

Summary: By using coupled amplitude-phase formulation, we construct the quartic anharmonic oscillator equation from the coupled higher order nonlinear Schrödinger equation. For arbitrary physical parameter values, we discuss the construction of new cnoidal wave solutions and the exact solutions of both bright and dark solitary waves. In addition, we investigate the pairs of dark-dark and bright-bright solitary waves.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
78A60 Lasers, masers, optical bistability, nonlinear optics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Agrawal, G.P., Nonlinear fiber optics, (2001), Academic Press San Diego
[2] Kodama, Y.; Hasegawa, A., Solitons in optical communications, (1995), Oxford University Press Oxford · Zbl 0840.35092
[3] Hasegawa, A.; Tappert, F., Appl phys lett, 23, 142, (1973)
[4] Hasegawa, A.; Tappert, F., Appl phys lett, 23, 171, (1973)
[5] Mollenauer, L.F.; Stolen, R.H.; Gordon, J.P., Phys rev lett, 45, 1095, (1980)
[6] Kodama, Y.; Hasegawa, A., IEEE J quant electron, QE, 23, 510, (1987)
[7] Mihalache, D.; Truta, N.; Crasovan, L.C., Phys rev E, 56, 1064, (1997)
[8] Emplit, P.; Hamaide, J.P.; Reynaud, F.; Froehley, C.; Barthelemy, A., Opt commun, 62, 374, (1987)
[9] Krökel, D.; Halas, N.J.; Giuliani, G.; Grischkowsky, D., Phys rev lett, 60, 29, (1988)
[10] Blow, K.J.; Doran, N.J., Electron lett, 19, 429, (1983)
[11] Kivshar, Yu.S.; Luther-Davies, B., Phys rep, 298, 81, (1998)
[12] Kivshar, Yu.S.; Afanasjev, V.V., Phys rev A, 44, R1446, (1991)
[13] Mitschke, F.M.; Mollenauer, L.F., Opt lett, 11, 659, (1986)
[14] Gedalin, M.; Scott, T.C.; Band, Y.B., Phys rev lett, 78, 448, (1997)
[15] Manakov, S.V., Sov phys JETP, 38, 248, (1974)
[16] Wadati, M.; Iizuka, T.; Hisakado, M., J phys soc jpn, 61, 2241-2245, (1992)
[17] Hisakado, M.; Iizuka, T.; Wadati, M., J phys soc jpn, 63, 2887-2894, (1994)
[18] Radhakrishnan, R.; Lakshmanan, M., Phys rev E, 54, 2950, (1996)
[19] Nakkeeran, K.; Porsezian, K.; Shanmugha Sundaram, P.; Mahalingam, A., Phys rev lett, 80, 1425, (1998)
[20] Sakovich, A.Yu.; Tsuchida, T., J phys A: math gen, 33, 7217, (2000)
[21] Mahalingam, A.; Porsezian, K., Phys rev E, 64, 46608, (2001)
[22] Gilson, C.; Hietarinta, J.; Nimmo, J.; Ohta, Y., Phys rev E, 68, 016614, (2003)
[23] Q-Han, Park; Shin, H.J., Phys rev E, 61, 3093, (2000)
[24] Chen, C.J.; Menyuk, C.R.; Islam, M.N.; Stolen, R.H., Opt lett, 16, 1647, (1991)
[25] Shan-liang, Liu; Xi-qiang, Liu, Phys lett A, 225, 67, (1997)
[26] Palacios, S.L.; Guinea, A.; Diaz, J.M.F.; Crespo, R.D., Phys rev E, 60, R45, (1996)
[27] Hioe, F.T., Phys rev E, 56, 7253, (1997)
[28] Fan, E.; Hon, Y.C., Chaos, solitons & fractals, 15, 559, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.