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Title: The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions

Abstract

The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form {nu}{partial_derivative}a({tau})/{partial_derivative}{tau}=a({tau}) -a{sup 2}({tau}- 1) a({tau}- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.

Authors:
 [1]
  1. Institute of Physics, West Pomeranian University of Technology, Szczecin (Poland)
Publication Date:
OSTI Identifier:
22043475
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 18; Journal Issue: 9; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL EQUATIONS; NUMERICAL ANALYSIS; PARTICLES; PLASMA; SIMULATION

Citation Formats

Marczynski, Slawomir. The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions. United States: N. p., 2011. Web. doi:10.1063/1.3639135.
Marczynski, Slawomir. The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions. United States. doi:10.1063/1.3639135.
Marczynski, Slawomir. Thu . "The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions". United States. doi:10.1063/1.3639135.
@article{osti_22043475,
title = {The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions},
author = {Marczynski, Slawomir},
abstractNote = {The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form {nu}{partial_derivative}a({tau})/{partial_derivative}{tau}=a({tau}) -a{sup 2}({tau}- 1) a({tau}- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.},
doi = {10.1063/1.3639135},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 9,
volume = 18,
place = {United States},
year = {2011},
month = {9}
}