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Optical and Quantum Electronics

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01-09-2014

Solitons for the cubic-quintic nonlinear Schrödinger equation with Raman effect in nonlinear optics

Authors: Ping Wang, Tao Shang, Li Feng, Yingjie Du

Published in: Optical and Quantum Electronics | Issue 9/2014

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Abstract

Considering the ultrashort optical soliton propagation in the non-Kerr media, the cubic-quintic nonlinear Schrödinger equation with Raman effect is studied through the dependent variable transformation and Hirota method. Based on symbolic computation, the bilinear form, the explicit one- and two-soliton solutions for the equation are presented. The constraint parametric condition for the existence of soliton solutions is also derived. Propagation characteristics and interaction behaviors of the solitons are graphically shown and discussed: (1) Overtaking elastic interactions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) propagation in parallel of the two solitons.

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Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, New York (1991)CrossRefMATH

Agrawal, G.P.: Nonlinear Fiber Optics, 4th edn. Academic Press, San Diego (2007)

Alka Goyal, A., Gupta, R., Kumar, C.N., Raju, T.S.: Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A 84, 0638309-1–0638309-6 (2011)

Calogero, F., Eckhaus, W.: Nonlinear evolution equations, rescalings, model PDES and their integrability: I. Inverse Probl. 3, 229–262 (1987)ADSCrossRefMATHMathSciNet

Chegini, N.G., Salaripanah, A., Mokhtari, R., Isvand, D.: Numerical solution of the regularized long wave equation using nonpolynomial splines. Nonlinear Dyn. 69, 459–471 (2012)CrossRefMATHMathSciNet

Clarkson, P.A., Tuszynski, J.A.: Exact solutions of the multidimensional derivative nonlinear Schrödinger equation for many-body systems near criticality. J. Phys. A 23, 4269–4288 (1990)ADSCrossRefMATHMathSciNet

Fanjoux, G., Michaud, J., Delqué, M., Furfaro, L., Maillotte, H., Sylvestre, T.: Spatio-temporal dynamics of multicolor spatial Kerr solitons. Opt. Quantum Electron. 40, 271–279 (2008)CrossRef

Gedalin, M., Scott, T.C., Band, Y.B.: Optical solitary waves in the higher order nonlinear Schrödinger equation. Phys. Rev. Lett 78, 448–451 (1997)ADSCrossRef

Hirota, R.: Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192–1194 (1971)ADSCrossRefMATH

Johnson, R.S.: On the modulation of water waves in the neighbourhood of kh\(\approx \)1.363. Proc. R. Soc. Lond. A 357, 131–141 (1977)ADSCrossRefMATH

Kim, W.S., Moon, H.T.: Soliton-kink interactions in a generalized nonlinear Schrödinger system. Phys. Lett. A 266, 364–369 (2000)ADSCrossRefMATHMathSciNet

Kodama, Y.: Optical solitons in a monomode fiber. J. Stat. Phys. 39, 597–614 (1985)ADSCrossRefMathSciNet

Kundu, A.: Landau-Lifeshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger equation-type equations. J. Math. Phys. 25, 3433–3438 (1984)ADSCrossRefMathSciNet

Liu, W.J., Tian, B.: Symbolic computation on soliton solutions for variable-coefficient nonlinear Schrödinger equations in nonlinear optics. Opt. Quantum Electron. 43, 147–162 (2012)CrossRefMathSciNet

Lü, X., Peng, M.S.: Nonautonomous motion study on accelerated and decelerated solitons for the variable-coefficient Lenells-Fokas model. Chaos 23, 013122-1–013122-7 (2013)ADS

Menezes, J.W.M., Sousa, J.R.R., Fraga, W.B., Lopes, V.C.M., Lima, F.T., Sobrinho, C.S., Sombra, A.S.B.: Spatiotemporal optical solitons in planar waveguide with periodically modulated cubic-quintic nonlinearity. Opt. Quantum Electron. 42, 179–192 (2010)CrossRef

Mitschkem, F.M., Mollenauer, L.F.: Discovery of the soliton self-frequency shift. Opt. Lett. 11, 659–661 (1986)ADSCrossRef

Pushkarov, D.I., Tanev, S.: Bright and dark solitary wave propagation and bistability in the anomalous dispersion region of optical waveguides with third- and fifth-order nonlinearities. Opt. Commun. 124, 354–364 (1996)ADSCrossRef

Qi, F.H., Tian, B., Lü, X., Guo, R., Xue, Y.S.: Darboux transformation and soliton solutions for the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics. Commun. Nonlinear. Sci. Numer. Simul. 17, 2372–2381 (2011)ADSCrossRef

Radhakrishnan, R., Kundu, A., Lakshmanan, M.: Coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity: Integrability and soliton interaction in non-Kerr media. Phy. Rev. E 60, 3314–3323 (1999)ADSCrossRef

Sarma, A.K.: Solitary wave solutions of higher-order NLSE with Raman and self-steepening effect in a cubic-quintic-septic medium. Commun. Nonlinear Sci. Numer. Simul. 14, 3215–3219 (2009)ADSCrossRef

Skarka, V., Berezhiani, V.I., Miklaszewski, R.: Spatiotemporal soliton propagation in saturating nonlinear optical media. Phys. Rev. E 56, 1080–1087 (1997)ADSCrossRef

Soto-Crespo, J.M., Pesquera, L.: Analytical approximation of the soliton solutions of the quintic complex Ginzburg-Landau equation. Phys. Rev. E. 56, 7288–7293 (1997)ADSCrossRef

Sun, Z.Y., Gao, Y.T., Yu, X., Liu, W.J., Liu, Y.: Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations. Phys. Rev. E 80, 066608-1–066608-11 (2009)ADS

Tian, B., Gao, Y.T.: Variable-coefficient higher-order nonlinear Schrödinger model in optical fibers: New transformation with burstons, brightons and symbolic computation. Phys. Lett. A 359, 241–248 (2006)ADSCrossRef

Wang, M.L., Zhang, J.L., Li, X.Z.: Solitary wave solutions of a generalized derivative nonlinear Schrödinger equation. Commun. Theor. Phys. 50, 39–42 (2008)ADSCrossRefMathSciNet

Wang, P., Tian, B.: Symbolic computation on the bright soliton solutions for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity. Opt. Commun. 285, 3567–3577 (2012a)ADSCrossRefMathSciNet

Wang, P., Tian, B.: Symbolic computation on soliton dynamics and Bäcklund transformation for the generalized coupled nonlinear Schrödinger equations with cubic-quintic nonlinearity. J. Mod. Opt. 59, 1786–1796 (2012b)ADSCrossRef

Title: Solitons for the cubic-quintic nonlinear Schrödinger equation with Raman effect in nonlinear optics
Authors: Ping Wang
Tao Shang
Li Feng
Yingjie Du
Publication date: 01-09-2014
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 9/2014
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-013-9840-8

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