Interaction of plane Langmuir solitons

Abstract

The formation and interaction of Langmuir solitons is governed by the Schrödinger equation with a self-consistent potential. Generally, two kinds of interaction - quasi-static and dynamic - are considered. In the former case, the problem reduces to solving the Schrödinger equation with a cubic term, while in the latter, the self-consistent potential satisfies the wave equation. It is maintained that in the quasi-static description, solitons do not asymptotically interact with each other if uninteresting shifts of the soliton phases are disregarded. In the dynamic approach - which is physically more consistent - solitons may interact with each other and with acoustic waves. The article considers the problem of the interaction of two identical solitons moving towards each other. Semi-quantitative estimates have been used in order to determine the region of parameters in which fusion of solitons is possible. The numerical modelling results which refine the analytical estimates are discussed. The analysis shows that there is practically no region where the quasi-static approximation can be applied, since this approximation disregards the low-frequency motions which are fundamentally important for the process of Langmuir turbulence instability. The process of soliton formation from a non-symmetrical Langmuir-wave packet is investigated. A study is made of the influence of the boundary conditions, especially the periodic ones, on the formation and interaction of solitons. Applying numerical modelling, the authors show that great caution must be exercised in using the periodic boundary conditions for unbounded systems. Wave boundary conditions have been suggested.