Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of plasma physics

PHYSICA D-NONLINEAR PHENOMENA

卷:238

Article

Zarmi, Yair^1,2 

[1] Ben Gurion Univ Negev, Jacob Blaustein Inst Desert Res, IL-84990 Midreshet Ben Gurion, Israel

[2] Ben Gurion Univ Negev, Dept Phys, IL-84990 Midreshet Ben Gurion, Israel

关键词: Ion acoustic wave equations;    Perturbed KdV equation;    Normal Form;    Soliton interactions;   

DOI  :  10.1016/j.physd.2009.04.010

来源: Elsevier

【 摘 要 】

A new approach to the perturbative analysis of dynamical systems, which can be described approximately by soliton solutions of integrable non-linear wave equations, is employed in the case of small-amplitude solutions of the ion acoustic wave equations of plasma physics. Instead of pursuing the traditional derivation of a perturbed KdV equation, the ion velocity is written as a sum of two components: elastic and inelastic. In the single-soliton case, the elastic component is the full solution. In the multiple-soliton case, it is complemented by the inelastic component. The original system is transformed into two evolution equations: An asymptotically integrable Normal Form for ordinary KdV solitons, and an equation for the inelastic component. The zero-order term of the elastic component is a single-soliton or multiple-soliton solution of the Normal Form. The inelastic component asymptotes into a linear combination of single-soliton solutions of the Normal Form, with amplitudes determined by soliton interactions, plus a second-order decaying dispersive wave. Satisfaction of a conservation law by the inelastic component and of mass conservation by the disturbance to the ion density is determined solely by the initial data and/or boundary conditions imposed on the inelastic component. The electrostatic potential is a first-order quantity. It is affected by the inelastic component only in second order. The charge density displays a triple-layer structure. The analysis is carried out through the third order. (C) 2009 Elsevier B.V. All rights reserved.

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