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Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

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Abstract

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.

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Acknowledgments

We express our sincere thanks to all the members of our discussion group for their valuable suggestions. This work has been supported by the National Natural Science Foundation of China under Grant No. 11101421, the Special Foundation for Young Scientists of Institute of Remote Sensing and Digital Earth of Chinese Academy of Sciences under Grant No. Y1S01500CX, and the Scientific Research Project of Beijing Educational Committee (No. SQKM201211232016).

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Authors and Affiliations

  1. School of Information, Beijing Wuzi University, Beijing , 101149, China

    Feng-Hua Qi & Hong-Mei Ju

  2. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Xiang-Hua Meng

  3. State Key Laboratory of Remote Sensing Science Jointly Sponsored by the Institute of Remote Sensing and Digital Earth of Chinese Academy of Sciences and Beijing Normal University, Beijing, 100101, China

    Juan Li

  4. Demonstration Center, Spaceborne Remote Sensing National Space Administration, Beijing, 100101, China

    Juan Li

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  1. Feng-Hua Qi
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  2. Hong-Mei Ju
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  4. Juan Li
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Correspondence to Feng-Hua Qi.

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Qi, FH., Ju, HM., Meng, XH. et al. Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Nonlinear Dyn 77, 1331–1337 (2014). https://doi.org/10.1007/s11071-014-1382-5

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  • DOI: https://doi.org/10.1007/s11071-014-1382-5

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