Linear versus nonlinear dissipation for critical NLS equation

The focusing nonlinear Schrödinger equation at critical dimension is considered in the presence of a weak damping, either linear or involving a power of the wave intensity. Special attention is paid to the case of a diffusive damping term, that describes Landau damping for a low-frequency Alfvén wav...

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Published inPhysica. D Vol. 203; no. 3; pp. 167 - 184
Main Authors Passot, T., Sulem, C., Sulem, P.L.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.04.2005
Elsevier
Subjects
Exact sciences and technology
Nonlinear Schrödinger equation
Physics
Wave collapse
Weak dissipation
05.45. − a
42.65.Jx
Weak dissipation
52.35 Bj
52.35 Mw
Nonlinear Schrödinger equation
Wave collapse
Collapse
Alfven waves
42.65.Jx Nonlinear Schrödinger equation
Linear damping
Intensity
Photon absorption
Non linear phenomenon
05.45.-a
Landau damping
Non linear damping
Energy dissipation
Differential equations
Filamentation instabilities
Schroedinger equation
Models
Nonlinear optics
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Abstract The focusing nonlinear Schrödinger equation at critical dimension is considered in the presence of a weak damping, either linear or involving a power of the wave intensity. Special attention is paid to the case of a diffusive damping term, that describes Landau damping for a low-frequency Alfvén wave subject to filamentation instability. When compared with the nonlinear damping classically used to model multi-photon absorption in nonlinear optics, significant differences concerning the wave energy dissipation are numerically observed and interpreted by means of an asymptotic ODE model resulting from a modulation analysis of the solution near collapse. It is in particular shown that whereas for a nonlinear damping, dissipation is almost totally concentrated in the collapse events, it remains sizeable while the wave defocuses when the damping is linear.
AbstractList The focusing nonlinear Schrödinger equation at critical dimension is considered in the presence of a weak damping, either linear or involving a power of the wave intensity. Special attention is paid to the case of a diffusive damping term, that describes Landau damping for a low-frequency Alfvén wave subject to filamentation instability. When compared with the nonlinear damping classically used to model multi-photon absorption in nonlinear optics, significant differences concerning the wave energy dissipation are numerically observed and interpreted by means of an asymptotic ODE model resulting from a modulation analysis of the solution near collapse. It is in particular shown that whereas for a nonlinear damping, dissipation is almost totally concentrated in the collapse events, it remains sizeable while the wave defocuses when the damping is linear.
Author Sulem, C.
Passot, T.
Sulem, P.L.
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Cites_doi 10.1016/S0167-2789(99)00198-0
10.1137/S0036139999362609
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10.1016/S0375-9601(98)00744-0
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10.1016/S0370-1573(97)00092-6
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Issue 3
Keywords 05.45. − a
42.65.Jx
Weak dissipation
52.35 Bj
52.35 Mw
Nonlinear Schrödinger equation
Wave collapse
Collapse
Alfven waves
42.65.Jx Nonlinear Schrödinger equation
Linear damping
Intensity
Photon absorption
Non linear phenomenon
05.45.-a
Landau damping
Non linear damping
Energy dissipation
Differential equations
Filamentation instabilities
Schroedinger equation
Models
Nonlinear optics
Language English
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  publication-title: Physica D
  doi: 10.1016/S0167-2789(98)90022-7
– volume: 132
  start-page: 112
  year: 1988
  ident: 10.1016/j.physd.2005.03.011_bib11
  article-title: Turbulent dissipation rates and the random occurence of coherent events
  publication-title: Phys. Lett. A
  doi: 10.1016/0375-9601(88)90264-2
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Snippet The focusing nonlinear Schrödinger equation at critical dimension is considered in the presence of a weak damping, either linear or involving a power of the...
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SubjectTerms Exact sciences and technology
Nonlinear Schrödinger equation
Physics
Wave collapse
Weak dissipation
Title Linear versus nonlinear dissipation for critical NLS equation
URI https://dx.doi.org/10.1016/j.physd.2005.03.011
https://hal.science/hal-00388301
Volume 203
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