Stationary Solitary Waves Research Articles

Spiky Soliton in Circular Polarized Alfvén Wave

A new type of nonlinear evolution equation for the Alfven waves, propagating parallel to the magnetic field, is now registered to the completely integrable family of nonlinear evolution equations. In spite of the extensive studies of Kaup and Newell, and of Kawata and Inoue, these analysis have been dealing with solutions for restricted boundary conditions. The present paper presents full account of stationary solitary wave solutions for the plane wave boundary condition. The obtained results exhibit peculiar structure of spiky modulation of amplitude and phase, which arises from the derivative nonlinear coupling term. A nonlinear equation for complex amplitude associated with the carrier wave is shown to be a mixed type of nonlinear Schrodinger equation, having an ordinary cubic nonlinear Schrodinger equation, having an ordinary cubic nonlinear term and the derivative of cubic nonlinear term.

A Modified Korteweg de Vries Equation for Ion Acoustic Waves

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.