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Arrest of Langmuir wave collapse by quantum effects
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Arrest of Langmuir wave collapse by quantum effects

G. Simpson, C. Sulem and P. L. Sulem
Physical review. E, Statistical, nonlinear, and soft matter physics, v 80(5), pp 056405-056405
01 Nov 2009
DOI: https://doi.org/10.1103/PhysRevE.80.056405
PMID: 20365081
url
https://hal.archives-ouvertes.fr/hal-00457437/file/simpson2009.pdfView
Published, Version of Record (VoR)Open Access (License Unspecified),  Open
url
https://doi.org/10.1103/PhysRevE.80.056405View
Published, Version of Record (VoR) Open

Abstract

Physics, Fluids & Plasmas Physics, Mathematical Science & Technology Physical Sciences Physics
The arrest of Langmuir wave collapse by quantum effects, first addressed by Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz trial function method is revisited, using rigorous estimates and systematic asymptotic expansions. The absence of blow up for the so-called quantum Zakharov equations is proved in two and three dimensions, whatever the strength of the quantum effects. The time-periodic behavior of the solution for initial conditions slightly in excess of the singularity threshold for the classical problem is established for various settings in two space dimensions. The difficulty of developing a consistent perturbative approach in three dimensions is also discussed and a semiphenomenological model is suggested for this case.

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Web of Science research areas
Physics, Fluids & Plasmas
Physics, Mathematical
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