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

Marczyński S.

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

机译：Berk-Breizman方程的两种模式扩展：时滞微分方程和渐近解

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The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form vδa(τ)/δτ = a(τ) - a ~2 (τ - 1) a(τ - 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.

机译：将描述粒子驱动波模式演化的积分微分伯克-布里兹曼（BB）方程转换成简单的延迟微分方程，形式为vδa（τ）/δτ= a（τ）-a〜2（τ-1） a（τ-2）。此变换也适用于BB理论的两种模式扩展。给出了获得的解以及导出的渐近解析解和数值结果。

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《Physics of plasmas》 |2011年第9期|共5页
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Marczyński S.;
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The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions

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