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Nonlinear Schrödinger Equations with a Four-Well Potential in Two Dimensions: Bifurcations and Stability Analysis

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Nonlinear Science and Complexity

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Abstract

We report a full bifurcation diagram for trapped states in the two-dimensional (2D) nonlinear Schrödinger (NLS) equation with a symmetric four-well potential. Starting from the linear limit, we use a four-mode approximation to derive a system of ordinary differential equations, which makes it possible to trace the evolution of all trapped stationary modes, and thus to identify different branches of solutions bifurcating in the full NLS model. Their stability is examined within the framework of the linear stability analysis.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003-4515, USA

    C. Wang, G. Theocharis, P. G. Kevrekidis & N. Whitaker

  2. Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    D. J. Frantzeskakis

  3. Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens, 157 84, Greece

    B. A. Malomed

Authors
  1. C. Wang
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  2. G. Theocharis
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  3. P. G. Kevrekidis
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  4. N. Whitaker
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  5. D. J. Frantzeskakis
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  6. B. A. Malomed
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Corresponding author

Correspondence to P. G. Kevrekidis .

Editor information

Editors and Affiliations

  1. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    J.A. Tenreiro Machado

  2. Dept. of Mech. & Industr. Engineering, Southern Illinois Univ. Edwardsville, Edwardsville, 62026-1805, Illinois, USA

    Albert C.J. Luo

  3. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Ramiro S. Barbosa

  4. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Manuel F. Silva

  5. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Lino B. Figueiredo

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Wang, C., Theocharis, G., Kevrekidis, P.G., Whitaker, N., Frantzeskakis, D.J., Malomed, B.A. (2011). Nonlinear Schrödinger Equations with a Four-Well Potential in Two Dimensions: Bifurcations and Stability Analysis. In: Machado, J., Luo, A., Barbosa, R., Silva, M., Figueiredo, L. (eds) Nonlinear Science and Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_22

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  • DOI: https://doi.org/10.1007/978-90-481-9884-9_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9883-2

  • Online ISBN: 978-90-481-9884-9

  • eBook Packages: EngineeringEngineering (R0)

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