The asymptotic behaviour of the new nonlinear waves propagating in the transmission lines

We discuss the new nonlinear waves in plasmas, referring to two nonlinear transmission lines. First, the asymptotic solution of a nonlinear evolution equation derived from one line is described by the dark envelope soliton with the modulational stability by use of the reductive perturbation method. Since the nonlinear capacitance of this line corresponds to the Langmuir plasma density, the line explains the propagation of the nonlinear Langmuir density modulation. Second, the asymptotic solution of a new nonlinear evolution equation from the other transmission line is expressed in terms of the bright envelope soliton with the modulational instability. Since the nonlinear capacitance of this line corresponds to the ion plasma density, we find that the line describes the propagation of the nonlinear density modulation of the electrostatic ion acoustic wave in collisionless plasmas. These solutions show us a point of view to investigate the asymptotic behaviour of the physical systems where balance between the strong dispersion and the higher-order derivative nonlinearity is essential. (author)