Higher-order corrections to the Korteweg-de Vries Solitons in general plasmas

Abstract

A fully relativistic multi-component plasma is considered as a template system for generic plasmas, and a reductive perturbation analysis is applied to the system up to the second and the third order to obtain partial differential equations that describe the evolution of the first-order (ϕ ₁) and the second-order (ϕ ₂) electrostatic potential waves. The secular-free one-soliton solution of the derived equations is obtained by using Kodama and Taniuti’s method [J. Phys. Soc. Jpn. 45, 29898 (1978)]. The results of present paper are generic in the sense that they are independent of any specificity of the parameters of the physical system because they are derived without making any restrictive assumptions on the system parameters. The presented results are applicable to any kind of multi-component plasma system because all constituent species are treated on equal mathematical footings throughout the analyses until the final specification is made for the system parameters. The algebraic results are so general that they can even be applied to nonrelativistic plasmas when appropriate nonrelativistic approximations are made to the final expressions. Thus, the presented result can be considered as a template for the one-soliton solution that can used for a large class of different plasma systems. To demonstrate the utility of the template, we specialize the generic results to a relativistically hot electron-positron pair plasma where each species has a different temperature. The general result is also applied to a three-component plasma composed of a relativistically hot electron-positron pair plasma with small fraction of ions. The third order corrections to the KdV solitons of the examples are presented.