Nonlinear evolution of ion drift mode in a non-Maxwellian plasma having adiabatic trapping of generalized (r, q)-distributed electrons

The low-frequency ion drift mode is investigated in a warm electron-ion plasma by incorporating adiabatic trapping of generalized (r, q) distributed electrons. The gradients in background density and magnetic field are taken into account. Two different nonlinear partial differential equations are obtained by incorporating the fractional and quadratic nonlinearities. The solitary solutions of these nonlinear partial differential equations are obtained by using the functional variable method. The dynamical analysis is performed by plotting phase portraits of the drift modes in the presence of generalized (r, q) distributed trapped electrons by using the bifurcation theory of the dynamical planar system. It is shown that, depending on the boundary conditions, the dynamical systems of both trapped Gardner and trapped KdV equations admit nonlinear solitary and periodic solutions. Graphical analysis reveals that plasma parameters, such as the ion temperature Ti, the background electron distribution, and the parameters r and q of the generalized distribution (r, q), alter the characteristics of dynamical orbits and solitary solutions.