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Dynamics of a Higher-Order Ginzburg–Landau-Type Equation

In: Nonlinear Analysis, Differential Equations, and Applications

Author

Listed:
  • Theodoros P. Horikis

    (University of Ioannina)

  • Nikos I. Karachalios

    (University of Thessaly)

  • Dimitrios J. Frantzeskakis

    (University of Athens)

Abstract

We study possible dynamical scenarios associated with a higher-order Ginzburg–Landau-type equation. In particular, first we discuss and prove the existence of a limit set (attractor), capturing the long-time dynamics of the system. Then, we examine conditions for finite-time collapse of the solutions of the model at hand, and find that the collapse dynamics is chiefly controlled by the linear/nonlinear gain/loss strengths. Finally, considering the model as a perturbed nonlinear Schrödinger equation, we employ perturbation theory for solitons to analyze the influence of gain/loss and other higher-order effects on the dynamics of bright and dark solitons.

Suggested Citation

  • Theodoros P. Horikis & Nikos I. Karachalios & Dimitrios J. Frantzeskakis, 2021. "Dynamics of a Higher-Order Ginzburg–Landau-Type Equation," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 187-207, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-72563-1_9
    DOI: 10.1007/978-3-030-72563-1_9
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