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On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations

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  • Xu, Gui-qiong
  • Li, Zhi-bin

Abstract

It is proven that generalized coupled higher-order nonlinear Schrödinger equations possess the Painlevé property for two particular choices of parameters, using the Weiss–Tabor–Carnevale method and Kruskal’s simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests.

Suggested Citation

  • Xu, Gui-qiong & Li, Zhi-bin, 2005. "On the Painlevé integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1363-1375.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:5:p:1363-1375
    DOI: 10.1016/j.chaos.2005.04.007
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    Cited by:

    1. Belmonte-Beitia, Juan & Pérez-García, Víctor M. & Vekslerchik, Vadym, 2007. "Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1268-1277.
    2. El-Nahhas, A., 2009. "Analytic approximations for the one-loop soliton solution of the Vakhnenko equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2257-2264.
    3. Aydın, Ayhan, 2009. "Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 735-751.

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