Nonlinear Wave Propagation Through Cold Plasma

An exciting and extremely active area of research investigation during the past years has been the study of solitons and the related issue of the construction of solutions to a wide class of nonlinear equations. The concept of solitons has now become umbiquitous in modern nonlinear science and indeed can be found in various branches of physics. In nonlinear wave propagation through continuous media, steepening of waves arises due to nonlinearities which is balanced by dissipative or dispersive effects. Exciting and important discoveries were made in the nonlinear dynamics of dissipative and conservative systems. There are different methods to study nonlinear systems. The reductive perturbation method for the propagation of a slow modulation of a quasimonochromatic wave was first established by Taniuti and Washimi for the whistler wave in a cold plasma. This method was generalised to a wide class of nonlinear wave systems by Taniuty and Yajima. Kakutani and Ono [1], Kawahara and Taniuti [2] and Taniuti and Wei [3] have investigated the propagation of hydromagnetic waves through a cold collision free plasma using this reductive perturbation method. In the study of the asymptotic behaviour of nonlinear dispersive waves, Gardner and Morikava [4] were the first to introduce the scale transformation