Solitonic and chaotic behaviors for the nonlinear dust-acoustic waves in a magnetized dusty plasma

Abstract

A model for the nonlinear dust-ion-acoustic waves in a two-ion-temperature, magnetized dusty plasma is studied in this paper. Via the symbolic computation, one-, two- and N-soliton solutions are obtained. It is found that when μeμi<2Ti2Te2+TiTe, the soliton amplitude is positively related to μe, μi, Ti, Zd, and B0, but inversely related to Te and md, with Te, Ti, μe, and μi as the temperature of an electron, temperature of a positive ion, normalized initial density of electrons, and normalized initial density of positive ions, respectively, Zd, B0, and md as the charge number of a dust particle, strength of the static magnetic field, and mass of a dust particle, respectively. It is also found that the two solitons are always parallel during the propagation on the x − y, x − t, and y − t planes, where x, y, and z are the scaled spacial coordinates, and t is the retarded time. Upon the introduction of the driving force Γ(t), both the developed and weak chaotic motions as well as the effect of Γ(t) are explored. Via the phase projections and power spectra, we find the difference between the two chaotic motions roots in the relative magnitude of nonlinearity and external force. Increasing the frequency of the external force or the strength of the damped term can weaken the chaotic motions of such a forced model.