Some studies on nonlinear wave propagation in plasmas

Abstract

The study on the evolution of waves in plasmas has taken key position since it could be a powerful tool to diagnose the plasma and keeps a closed relation between the-ory and experiments. In the present decades, in contrast to the linear waves, the nonlinear wave dynamics become important in finding the various new features of plasma waves. The exciting and extremely active area of research on nonlinear wave phenomena becoming main interest in plasma dynamics as well as in other branches of physics and applied mathematics. The heuristic phenomena of plasma-acoustic mode obtained from the interaction of nonlinearity with the weak dispersive effect resulted the special characteristics of the wave known as soliton. Since its concept of the soliton evolution was established in plasma dynamics, the researchers have drawn their attention for new findings with a view to bridging the close relation be-tween theory and experiments. Further attention has also been focused to relate the observations in space plasma and other surrounding astrophysical problems. The mathematical formulation of the nonlinear wave equation has found to sustain a rich variety of nonlinear waves and extended the results for laboratory and space plasmas. Washimi and Taniuti [Phys. Rev. Lett. 17, 996 (1966)] were the first to derive the Korteweg-deVries(K-dV) equation based on reductive perturbation technique for studying the ion-acoustic solitary waves in plasmas. Thereafter, the technique becomes the subject of considerable interest to study the nonlinear waves in plasma and generalized to a wide class of nonlinear wave phenomena. In the same decade or later, the nonlinear waves have been studied by deriving the other forms on nonlinear wave equation, known as Nonlinear Schrodinger(NLS) equation, Sine-Gordon(S-G) equation, Boussinesq equation, Kadomtsev-Petviashvili(K-P) equation and Zakharov-Kuznetsov(Z-K) equation. Sagdeev [Rev. Plasma Phys. 4, 23 (1966)] also studied the nonlinear wave phenomena by using an alternate method known as...