A Modified Korteweg de Vries Equation for Ion Acoustic Waves

Abstract

Three wave mode coupling effects on ion acoustic waves are examined by applying the Fourier transformation method of separation of the nonlinear slow processes for a two component plasma described by the Vlasov equation. Contribution of the three mode coupling terms gives rise to a modified Korteweg de Vries equation with a nonlinear term of the form of { B φ+( C /2)φ 2 }φ x , where B and C are constants determined by the unperturbed state of plasmas. It is found that velocity of a stationary solitary wave depends sensitively on the electronion temperature ratio, and that the equation obtained here enables us to account for the amplitude dependence of the solitary wave velocity observed by Ikezi, Baker and Taylor.