Nonlinear cnoidal waves and solitary structures in unmagnetized plasmas with generalized (r, q) distributed electrons

Theoretical investigation of electrostatic ion acoustic periodic (cnoidal) waves and solitons with warm ions is presented with electrons that are assumed to follow the double spectral index distribution function. The double spectral index distribution imitates effectively the distributions that have often been seen in space plasmas. Using the standard reductive perturbation technique, the Korteweg-de Vries (KdV) equation is derived which describes the nonlinear periodic waves with appropriate boundary conditions. By using planar dynamical system to this KdV equation, the existence of solitary wave solutions and periodic wave solutions are found. It is shown that changing the electron population in regions of low and high phase space density regions alter the propagation characteristics of nonlinear ion acoustic periodic and solitary structures. Comparison of non-Maxwellian distribution functions with Maxwellian distribution is also made. The importance of the present work with regard to space plasmas is also pointed out.