Darboux transformation and soliton solutions for the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics. (English) Zbl 1335.35239

Summary: In this paper, by virtue of the Darboux transformation (DT) and symbolic computation, the quintic generalization of the coupled cubic nonlinear Schrödinger equations from twin-core nonlinear optical fibers and waveguides are studied, which describe the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media. Lax pair of the equations is obtained and the corresponding DT is constructed. Moreover, one-, two- and three-soliton solutions are presented in the forms of modulus. Features of solitons are graphically discussed: (1) head-on and overtaking elastic collisions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) energy-exchanging collisions of the three solitons.


35Q55 NLS equations (nonlinear Schrödinger equations)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35C08 Soliton solutions
Full Text: DOI


[1] Radhakrishnan, R.; Kundu, A.; Lakshmanan, M., Phys rev E, 60, 3, (1999)
[2] Porsezian, K.; Kuriakose, V.C.; Tian, B.; Gao, Y.T.; Zhu, H.W.; Liu, W.J.; Tian, B.; Zhang, H.Q.; Li, L.L.; Xue, Y.S.; Zhang, H.Q.; Xu, T.; Li, J.; Tian, B.; Lü, X.; Zhu, H.W.; Meng, X.H.; Yang, Z.C.; Tian, B., Optical solitons: theoretical and experimental challenges, Phys lett A, Phys rev E, Phys rev E, J math anal appl, 336, 1305, (2007), Springer New York
[3] Hasegawa, A.; Tappert, F., Appl phys lett, 23, 142, (1973)
[4] Mollenauer, L.F.; Stolen, R.H.; Gordon, J.P., Phys rev lett, 45, 1095, (1980)
[5] Hasegawa, A.; Kodama, Y., Solitons in optical communications, (1995), Oxford University New York · Zbl 0840.35092
[6] Islam, M.N., Ultrafast fiber switching devices and systems, (1992), Cambridge University England
[7] Newell, A.C.; Moloney, J.V., Nonlinear optics, (1992), Addison-Wesley New York
[8] Abdullaev, F.; Darmanyan, S.; Khabibullaev, P., Optical solitons, (1993), Springer-Verlag Berlin
[9] Zhang, J.L.; Wang, M.L.; Hong, W.P., Chaos solitons fract, Opt commun, 194, 217, (2001)
[10] Skarka, V.; Berezhiani, V.I.; Miklaszewski, R.; Afanasjev, V.V.; Chu, P.L.; Kivshar, Y.S., Phys rev E, Opt lett, 22, 1388, (1997)
[11] Dattoli, G.; Orisitto, F.P.; Toree, A., Opt lett, 14, 456, (1989)
[12] Zhu, S.D.; Mihalache, D.; Truta, N.; Crasovan, L.C.; Gedalin, M.; Scott, T.C.; Band, Y.B., Chaos solitons fract, Phys rev E, Phys rev lett, 78, 448, (1997)
[13] Yan, Z.Y., J phys soc jpn, 73, 2397, (2004)
[14] Zong, F.D.; Dai, C.Q.; Zhang, J.F., Commun theor phys, 45, 721, (2006)
[15] Kundu, A.; Calogero, F.; Eckhaus, W., J math phys, Inv prob, 3, 229, (1987)
[16] Levi, D.; Scimiterna, C., J phys A, 42, 465203, (2009)
[17] Wang, M.L.; Zhang, J.L.; Li, X.Z.; Clarkson, P.A.; Tuszynski, J.A., Commun theor phys, J phys A, 23, 4269, (1990)
[18] Johnson, R.S., Proc roy soc London A, 357, 131, (1977)
[19] Kodama, Y., J stat phys, 39, 597, (1985)
[20] Albuch, L.; Malomed, B.A., Math commun simul, 74, 312, (2007)
[21] Hisakado, M.; Wadati, M.; Hisakado, M.; Wadati, M., J phys soc jpn, J phys soc jpn, 64, 408, (1995)
[22] Barnett, M.P.; Capitani, J.F.; Von Zur Gathen, J.; Gerhard, J.; Tian, B.; Shan, W.R.; Zhang, C.Y.; Wei, G.M.; Gao, Y.T.; Tian, B.; Gao, Y.T., Int J quantum chem, Eur phys J.B (rapid not.), Phys lett A, 359, 241, (2006)
[23] Yan, Z.Y.; Zhang, H.Q.; Gao, Y.T.; Tian, B.; Gao, Y.T.; Tian, B.; Gao, Y.T.; Tian, B.; Gao, Y.T.; Tian, B.; Tian, B.; Wei, G.M.; Zhang, C.Y.; Shan, W.R.; Gao, Y.T., J phys A, Phys lett A, Phys plasmas, Phys plasmas (lett), Europhys lett, Phys lett A, 356, 8, (2006)
[24] Das, G.; Sarma, J.; Tian, B.; Gao, Y.T.; Tian, B.; Gao, Y.T.; Tian, B.; Gao, Y.T., Phys plasmas, Phys plasmas, Phys plasmas (lett), Phys lett A, 362, 283, (2007)
[25] Ablowitz, M.J.; Kaup, D.J.; Newell, A.C.; Segur, H., Phys rev lett, 31, 125, (1973)
[26] Gu CH, Hu HS, Zhou ZX. Darboux transformation in soliton theory and its geometric applications (Shanghai Sci-Tech, Shanghai, 2005)
[27] Fan EG. Computer algebra and integrable systems (Science, Beijing, 2004)
[28] Li, J.; Zhang, H.Q.; Xu, T.; Zhang, Y.X.; Hu, W.; Tian, B.; Lü, X.; Zhu, H.W.; Yao, Z.Z.; Meng, X.H.; Zhang, C.; Zhang, C.Y., J phys A, Ann phys (N.Y.), 323, 1947, (2008)
[29] Li YS. Soliton and integrable system (Shanghai Sci-Tech, Shanghai, 1999).
[30] Kim, W.S.; Moon, H.T.; Malomed, B.A.; Seong, N.H.; Kim, D.Y., Phys lett A, Phys rev A, Opt lett, 27, 1321, (2002)
[31] Haelterman, M.; Shepppard, A.; Sun, Z.Y.; Gao, Y.T.; Yu, X.; Liu, W.J.; Liu, Y., Phys rev E, Phys rev E, 80, 066608, (2009)
[32] Yu, X.; Gao, Y.T.; Sun, Z.Y.; Liu, Y.; Yu, X.; Gao, Y.T.; Sun, Z.Y.; Meng, X.H.; Liu, Y.; Feng, Q.; Sun, Z.Y.; Gao, Y.T.; Yu, X.; Liu, Y.; Wang, L.; Gao, Y.T.; Gai, X.L.; Sun, Z.Y.; Wang, L.; Gao, Y.T.; Gai, X.L., Phys rev E, J math anal appl, Colloid surface A, Phys scripta, Z naturforsch A, 65, 1, (2010), 519-27
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.