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Optical solitons, explicit solutions and modulation instability analysis with second-order spatio-temporal dispersion

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Abstract.

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the nonlinear Schrödinger equation (NLSE) with group velocity dispersion coefficient and second-order spatio-temporal dispersion coefficient, which arises in photonics and waveguide optics and in optical fibers. The integration algorithm is the sine-Gordon equation method (SGEM). Furthermore, the explicit solutions of the equation are derived by considering the power series solutions (PSS) theory and the convergence of the solutions is guaranteed. Lastly, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is obtained.

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Authors and Affiliations

  1. Firat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey

    Mustafa Inc, Aliyu Isa Aliyu & Abdullahi Yusuf

  2. Federal University Dutse, Science Faculty, Department of Mathematics, 7156, Jigawa, Nigeria

    Aliyu Isa Aliyu & Abdullahi Yusuf

  3. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  4. Institute of Space Sciences, Magurele, Romania

    Dumitru Baleanu

Authors
  1. Mustafa Inc
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  2. Aliyu Isa Aliyu
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  3. Abdullahi Yusuf
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  4. Dumitru Baleanu
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Correspondence to Mustafa Inc.

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Inc, M., Isa Aliyu, A., Yusuf, A. et al. Optical solitons, explicit solutions and modulation instability analysis with second-order spatio-temporal dispersion. Eur. Phys. J. Plus 132, 528 (2017). https://doi.org/10.1140/epjp/i2017-11812-2

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