Abstract In this thesis, we have investigated the nonlinear dynamics of lowfrequency electrostatic/electromagnetic waves in a nonuniform electronpositronion (epi) magnetoplasma with sheared ion flows. The ion dynamics is governed by the ion continuity and momentum balance equations, whereas the electrons and positrons are assumed to follow Boltzmann distributions, for electrostatic case. It is shown that the lowfrequency ionacoustic and electrostaticdrift waves can become unstable due to the ion sheared flow. In a collisional case a driftdissipative instability can also take place. For the nonlinear case, it is shown that a quasistationary solution of the mode coupling equations can be represented in the form of monopolar vortex. We have also generalized the said work by considering non uniform strongly magnetized electronpositron plasma with finite iontemperature effect and in the presence of sheared ion flows. In the linear limit, a dispersion relation is obtained that admits new instability of driftwaves. Whereas, the nonlinear interaction between the finite amplitude shortwavelength waves give rise to quadrupolar vortices. We have extended our earlier studies to the iontemperaturegradient (lTO) driven electrostatic waves in a collisionless epi magnetoplasma that contain equilibrium density, temperature, magnetic field, velocity and electrostatic potential gradients. We thus use hydrodynamic equations under driftapproximation and derive a set of non linear equations composed of ion continuity, the ion equation of motion and ion energy balance equations. In the linear limit, it is shown that nonzero equilibrium iontemperaturegradient and the presence of positrons modify the basic drift modes. On the other hand, in the nonlinear case, it is shown that under certain conditions possible stationary solutions of the same set of nonlinear equations are reduced in the form of various types of vortex patterns. We have also incorporated the selfgravitational effect of ions in this work and have shown that possible stationary solutions of the nonlinear equations can be represented in the form of dipolar and tripolar vortices of gravitational potential. Furthermore, we have also extended our study of electrostatic ITO modes to the electromagnetic case and derived a new set of coupled nonlinear equations which governs the dynamics of lowfrequency electromagnetic ITOdriven modes in a nonuniform electronpositronion magnetoplasma with nonzero iontemperaturegradients. We reexamined nonlinear mode coupling equations under various approximations. In the linear limit, a local dispersion relation has been derived and analyzed in several interesting limiting cases. On the other hand, a quasistationary solution of the mode coupling equations in the absence of collisions can be represented in the form of dipolar and vortexchain solutions. Finally, we have studied the temporal behavior of electrostatic/electromagnetic ITG modes in epi magnetoplasma and showed that the mode coupling equations can be represented in the form of wellknown Lorenz and Stenflo type equations that admit chaotic trajectories. The results of our investigations are helpful to understand the wave phenomena in laboratory and astrophysical plasmas.
