English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

A new approach to the perturbative analysis of dynamical systems, which canbe described approximately by soliton solutions of integrable nonlinear waveequations, is employed in the case of small-amplitude solutions of the ionacoustic wave equations of Plasma Physics. Instead of the traditionalderivation of a perturbed KdV equation, the ion velocity is written as a sum oftwo components: elastic and inelastic. In the single-soliton case, the elasticcomponent is the full solution. In the multiple-soliton case, it iscomplemented by the inelastic component. The original system is transformedinto two evolution equations: An asymptotically integrable Normal Form forordinary KdV solitons, and an equation for the inelastic component. Thezero-order term of the elastic component is a single- ormultiple-soliton-solution of the Normal Form. The inelastic componentasymptotes into a linear combination of single-soliton solutions of the NormalForm, with amplitudes determined by soliton interactions, plus a second-orderdecaying dispersive wave. Satisfaction of a conservation law by the inelasticcomponent and of mass conservation by the disturbance to the ion density isdetermined solely by the initial data and/or boundary conditions imposed on theinelastic component. The electrostatic potential is a first-order quantity. Itis affected by the inelastic component only in second-order. The charge densitydisplays a triple-layer structure. The analysis is carried out through thirdorder.

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