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Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures

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  • Belmonte-Beitia, Juan
  • Pérez-García, Víctor M.
  • Vekslerchik, Vadym

Abstract

In this paper, we study a system of coupled nonlinear Schrödinger equations modelling a quantum degenerate mixture of bosons and fermions. We analyze the stability of plane waves, give precise conditions for the existence of solitons and write explicit solutions in the form of periodic waves. We also check that the solitons observed previously in numerical simulations of the model correspond exactly to our explicit solutions and see how plane waves destabilize to form periodic waves.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:4:p:1268-1277
    DOI: 10.1016/j.chaos.2005.12.043
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    References listed on IDEAS

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    1. Dai, Chaoqing & Zhang, Jiefang, 2006. "Jacobian elliptic function method for nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1042-1047.
    2. 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.
    3. Mohamadou, Alidou & Kenfack-Jiotsa, A. & Kofané, T.C., 2006. "Modulational instability and spatiotemporal transition to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 914-925.
    4. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
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    Cited by:

    1. Gerdjikov, V.S. & Kostov, N.A. & Doktorov, E.V. & Matsuka, N.P., 2009. "Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 112-119.
    2. Belmonte-Beitia, Juan, 2009. "Exact solutions for the quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1005-1009.

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