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Collision dynamics of elliptically polarized solitons in Coupled Nonlinear Schrödinger Equations

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  • Todorov, M.D.
  • Christov, C.I.

Abstract

We investigate numerically the collision dynamics of elliptically polarized solitons of the System of Coupled Nonlinear Schrödinger Equations (SCNLSE) for various different initial polarizations and phases. General initial elliptic polarizations (not sech-shape) include as particular cases the circular and linear polarizations. The elliptically polarized solitons are computed by a separate numerical algorithm. We find that, depending on the initial phases of the solitons, the polarizations of the system of solitons after the collision change, even for trivial cross-modulation. This sets the limits of practical validity of the celebrated Manakov solution. For general nontrivial cross-modulation, a jump in the polarization angles of the solitons takes place after the collision (‘polarization shock’). We study in detail the effect of the initial phases of the solitons and uncover different scenarios of the quasi-particle behavior of the solution. In majority of cases the solitons survive the interaction preserving approximately their phase speeds and the main effect is the change of polarization. However, in some intervals for the initial phase difference, the interaction is ostensibly inelastic: either one of the solitons virtually disappears, or additional solitons are born after the interaction. This outlines the role of the phase, which has not been extensively investigated in the literature until now.

Suggested Citation

  • Todorov, M.D. & Christov, C.I., 2012. "Collision dynamics of elliptically polarized solitons in Coupled Nonlinear Schrödinger Equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1321-1332.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:7:p:1321-1332
    DOI: 10.1016/j.matcom.2010.04.022
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    References listed on IDEAS

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    1. Todorov, M.D. & Christov, C.I., 2009. "Impact of the large cross-modulation parameter on the collision dynamics of quasi-particles governed by vector NLSE," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 46-55.
    2. Sonnier, W.J. & Christov, C.I., 2005. "Strong coupling of Schrödinger equations: Conservative scheme approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 69(5), pages 514-525.
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    Cited by:

    1. Gerdjikov, V.S. & Todorov, M.D. & Kyuldjiev, A.V., 2016. "Asymptotic behavior of Manakov solitons: Effects of potential wells and humps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 166-178.
    2. Todorov, M.D., 2016. "The effect of the elliptic polarization on the quasi-particle dynamics of linearly coupled systems of Nonlinear Schrödinger Equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 273-286.

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