The routes to stability of spatially periodic solutions of the linearly damped NLS equation

Spatially periodic breather solutions (SPBs) of the nonlinear Schrödinger (NLS) equation, i.e., the heteroclinic orbits of unstable Stokes waves, are typically unstable. In this paper, we study the effects of dissipation on single-mode and multi-mode SPBs using a linearly damped NLS equation. The nu...

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Bibliographic Details
Published in:European physical journal plus 2020-08, Vol.135 (8), p.642, Article 642
Main Authors: Schober, C. M., Islas, A.
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Boundary conditions
Complex Systems
Condensed Matter Physics
Damping
Experiments
Focus Point on Solitons
Integrability
Mathematical and Computational Physics
Molecular
Nonlinear Waves: Theory and Applications
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Spectral theory
Stability
Theoretical
Water waves
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Summary:Spatially periodic breather solutions (SPBs) of the nonlinear Schrödinger (NLS) equation, i.e., the heteroclinic orbits of unstable Stokes waves, are typically unstable. In this paper, we study the effects of dissipation on single-mode and multi-mode SPBs using a linearly damped NLS equation. The number of instabilities the background Stokes wave possesses and the damping strength are varied. Viewing the damped dynamics as near integrable, the perturbed flow is analyzed by appealing to the spectral theory of the NLS equation. A broad categorization of the routes to stability of the SPBs and how the route depends on the mode structure of the SPBs and the instabilities of the Stokes wave is obtained as well as the distinguishing features of the damped flow.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-020-00660-w