Explosion of soliton in a multicomponent plasma

Abstract

A three-dimensional nonlinear Kadomtsev–Petviashvili (K–P) wave equation is derived to discuss the solitons in multicomponent plasma contaminated with negative ions. A new formalism of the simple wave solution method is developed for finding the soliton behaviors caused by the presence of negative ions in plasmas. It is seen that the nonlinear wave equation leads, in some cases, to an ordinary differential equation and a straight way for solving the soliton propagation in plasmas. The overall observations describe the natures of compressive and rarefactive solitons along with the shock-like wave caused by the interaction of negative ions. Also discussed are the possible controls of the scenarios of soliton behaviors. Moreover it is believed, from present investigations, that the observations of collapses or explosions in solitons could enhance the understanding of the soliton phenomena in laboratory and space plasmas.

Nonlinear Ion‐Acoustic Solitary Waves and Double Layers in Multicomponent Plasmas

“…However, this technique, by now, is well established in fluid dynamics in finding the wave solution in inhomogeneous fluid and later many investigators (Ianenko [20]; Pogodin et al [21]; Das [22]) employed this technique to study the acoustic gravity waves in atmosphere. ,The same procedure, with slight modification, has been adopted t o solve the nonlinear wave equation (Das et al [19]) derived in a multicomponent plasma and have shown the novelty of the method to find the nonlinear structure that appears in plasma acoustic waves, Our motivation is to propose the same approach to find the complete soliton solution of the NIK-dV equation. To apply this procedure we use the following transformation…”

“…On the other hand, Jones et al [lo] considered a plasma with multi-temperature electrons and has shown that, even for a small percentage of additional multi-temperature electrons, there exist new features in the plasma acoustic modes. However, the salient features of solitons were further studied theoretically by many authors through the derivation of K-dV or K-P [19]). …”

“…To show the novelty of deriving the soliton solution of equation (9), we propose the modified method, adopted recently by Das e t al. [19] known as simple wave solution technique. However, this technique, by now, is well established in fluid dynamics in finding the wave solution in inhomogeneous fluid and later many investigators (Ianenko [20]; Pogodin et al [21]; Das [22]) employed this technique to study the acoustic gravity waves in atmosphere.…”

“…which is the soliton solution of a simple K-dV equation derived in isothermal plasma (called as IK-dV equation) and the solution, by using the tanh-method, has been recently discussed expeditiously by Das et al [19], where they have taken the plasma model with negative ions, due to which the nonlinearity, A admits a zero at which the solution either explodes or collapses depending on the energy conservation in the waves. The overall feature depends on the nonlinearity A , controlled by the plasma parameters.…”

Comment on “A new mathematical approach for finding the solitary waves in dusty plasma” [Phys. Plasmas 5, 3918 (1998)]

“…͑1͒ Of the misleading statements in their paper, the worst is the claim by the authors that the tanh-method, as a novel and simple way of obtaining solitary wave solutions of nonlinear evolution equations in plasma physics, was developed by Das et al 2 Of course, and as is indeed mentioned, the tanh-method and variations thereof have been known in fluid dynamics for a long time, where they amount to a useful rephrasing of properties of the underlying Legendre polynomial structures. In the present context, the tanh-method refers to a technique to find closed-form solutions of nonlinear partial differential equations ͑PDE͒ as polynomials in the ͑independent͒ variable Y ϭtanh , rather than in the wave argument ϭkxϪ tϩ␦ itself.…”