Quasi-periodic and chaotic structure of Alfvén waves in a plasma containing double spectral distributed electrons

The nonlinear characteristics of Alfvén waves in a plasma medium composed of double spectral electron distribution and positive and negative ions are investigated. A Korteweg–de Vries (KdV-type) equation is derived using the reductive perturbation technique. The periodic and soliton structures are investigated. The effects of the two spectral indices r and q on the produced periodic structures are studied. It is found that the amplitude of the rarefactive periodic wave increases by increasing the values of r and q. Some external perturbation intruders on the system are considered, and the quasi periodic and chaotic structures of Alfvén waves are discussed. It is found that by decreasing the values of [Formula: see text] (knowing that β known as the ratio of kinetic to magnetic pressures), the periodic structure is converted gradually into chaotic structure passing through the quasi-periodic one. The results of this study are helpful in describing the behavior of the Alfvénic structure of periodic waves and other related events in the ionosphere region.