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

Theodoros P. Horikis (), Nikos I. Karachalios () and Dimitrios J. Frantzeskakis ()
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Theodoros P. Horikis: University of Ioannina
Nikos I. Karachalios: University of Thessaly
Dimitrios J. Frantzeskakis: University of Athens

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 187-207 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_9

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DOI: 10.1007/978-3-030-72563-1_9

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