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Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion

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Abstract

This work studies the optical solitons with time-modulated nonlinearities and spatiotemporal dispersion. Four types of nonlinearity—Kerr law nonlinearity, parabolic law nonlinearity, power law nonlinearity, and dual-power law nonlinearity—are considered. The non-auto-Bäcklund transformation is obtained. Analytical soliton solutions are constructed. The presented results can be applied in the area of dispersion- and nonlinearity-managed solitons.

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References

  1. Zhong, W.P., Belić, M.: Breather solutions of the generalized nonlinear Schrödinger equation with spatially modulated parameters and a special external potential. Eur. Phys. J. Plus 129, 1 (2014)

    Article  Google Scholar 

  2. Yan, Z., Dai, C.: Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients. J. Opt. 15, 064012 (2013)

    Article  Google Scholar 

  3. Belmonte-Beitia, J., Pérez-García, V.M.: Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities. Phys. Rev. Lett. 98, 064102–064105 (2007)

    Article  Google Scholar 

  4. Dai, C.Q., Wang, Y.Y., Tian, Q., Zhang, J.F.: The management and containment of self-similar rogue waves in the inhomogeneous nonlinear Schrödinger equation. Ann. Phys. 327, 512 (2012)

    Article  MATH  Google Scholar 

  5. Triki, H., Hayat, T., Aldossary, O.M., Biswas, A.: Bright and dark solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients. Opt. Laser Technol. 44, 2223 (2012)

    Article  Google Scholar 

  6. Triki, H., Wazwaz, A.M.: A one-soliton solution of the ZK (m, n, k) equation with generalized evolution and time-dependent coefficients. Nonlinear Anal. Real 12, 2822 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Eslami, M., Mirzazadeh, M., Fathi Vajargah, B., Biswas, A.: Optical solitons for the resonant nonlinear Schrödinger’s equation with time-dependent coefficients by the first integral method. Optik 125, 3107 (2014)

    Article  Google Scholar 

  8. Zhou, Q., Zhu, Q., Bhrawy, A.H., Moraru, L., Biswas, A.: Optical solitons with spatially-dependent coefficients by Lie symmetry. Optoelectron. Adv. Mater. 8, 800 (2014). (2014)

    Google Scholar 

  9. Wazwaz, A.M., Triki, H.: Soliton solutions for a generalized KdV and BBM equations with time-dependent coefficients. Commun. Nonlinear Sci. Numer. Simul. 16, 1122 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  10. Triki, H., Wazwaz, A.M.: Traveling wave solutions for fifth-order KdV type equations with time-dependent coefficients. Commun. Nonlinear Sci. Numer. Simul. 19, 404 (2014)

    Article  MathSciNet  Google Scholar 

  11. Belmonte-Beitia, J., Pérez-García, V.M., Vekslerchik, V., Konotop, V.V.: Localized nonlinear waves in systems with time- and space-modulated nonlinearities. Phys. Rev. Lett. 100, 164102 (2008)

    Article  Google Scholar 

  12. Tian, B., Gao, Y.T.: Symbolic-computation study of the perturbed nonlinear Schrödinger model in inhomogeneous optical fibers. Phys. Lett. A 342, 228 (2005)

    Article  MATH  Google Scholar 

  13. Tang, X.Y., Shukla, P.K.: Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with an external potential. Phys. Rev. A 76, 013612 (2007)

    Article  MathSciNet  Google Scholar 

  14. Tian, Q., Wu, L., Zhang, J.F., Malomed, B.A., Mihalache, D., Liu, W.M.: Exact soliton solutions and their stability control in the nonlinear Schrödinger equation with spatiotemporally modulated nonlinearity. Phys. Rev. E 83, 016602 (2011)

    Article  MathSciNet  Google Scholar 

  15. Biswas, A., Cleary, C., Watson Jr, J.E., Milovic, D.: Optical soliton perturbation with time-dependent coefficients in a log law media. Appl. Math. Comput. 217, 2891 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  16. Eslami, M., Mirzazadeh, M., Biswas, A.: Soliton solutions of the resonant nonlinear Schrödinger’s equation in optical fibers with time-dependent coefficients by simplest equation approach. J. Mod. Opt. 60, 1627 (2013)

    Article  Google Scholar 

  17. Saha, M., Sarma, A.K.: Solitary wave solutions and modulation instability analysis of the nonlinear Schrodinger equation with higher order dispersion and nonlinear terms. Commun. Nonlinear Sci. Numer. Simul. 18, 2420 (2013)

  18. Zhou, Q.,  Zhu, Q.:  Optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Waves Random Complex Media (in press). doi:10.1080/17455030.2014.956847

  19. Savescu, M., Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Khan, K.R., Mahmood, M.F., Biswas, A.: Optical solitons in nonlinear directional couplers with spatio-temporal dispersion. J. Mod. Opt. 61, 441 (2014)

  20. Savescu, M., Hilal, E.M., Alshaery, A.A., Bhrawy, A.H., Moraru, L., Biswas, A.: Optical solitons with quadratic nonlinearity and spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16, 619 (2014)

    Google Scholar 

  21. Biswas, A., Khalique, C.M.: Stationary solutions for nonlinear dispersive Schrödinger’s equation. Nonlinear Dyn. 63, 623 (2011)

    Article  MathSciNet  Google Scholar 

  22. Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Milovic, D., Moraru, L., Savescu, M., Biswas, A.: Optical solitons with polynomial and triple-power law nonlinearities and spatio-temporal dispersion. Proc. Rom. Acad. Ser. A 235 (2014)

  23. Zhou, Q.: Analytic study on solitons in the nonlinear fibers with time-modulated parabolic law nonlinearity and Raman effect. Optik 125, 3142 (2014)

    Article  Google Scholar 

  24. Zhou, Q., Zhu, Q., Liu, Y., Yu, H., Yao, P., Biswas, A.: Thirring optical solitons in birefringent fibers with spatio-temporal dispersion and Kerr law nonlinearity. Laser Phys. 25, 015402 (2015)

    Article  Google Scholar 

  25. Zhou, Q., Zhu, Q., Yu, H., Liu, Y., Wei, C., Yao, P., Bhrawy, A.H., Biswas, A.: Bright, dark and singular optical solitons in a cascaded system. Laser Phys. 25, 015402 (2015)

    Article  Google Scholar 

  26. Zhou, Q., Yao, D., Chen, F.: Analytical study of optical solitons in media with Kerr and parabolic-law nonlinearities. J. Mod. Opt. 60, 1652 (2013)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The research was supported by the Scientific Research Fund of Hubei Provincial Education Department (Grant No. B2013193).

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, People’s Republic of China

    Qin Zhou, Qiuping Zhu, Hua Yu & Xuanming Xiong

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  1. Qin Zhou
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  2. Qiuping Zhu
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  3. Hua Yu
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  4. Xuanming Xiong
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Correspondence to Qin Zhou.

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Zhou, Q., Zhu, Q., Yu, H. et al. Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion. Nonlinear Dyn 80, 983–987 (2015). https://doi.org/10.1007/s11071-015-1922-7

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  • DOI: https://doi.org/10.1007/s11071-015-1922-7

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