By using Braginskii transport equations for ions and Boltzmann distribution for electrons, a new system of nonlinear equations governing the dynamics of low-frequency, short-wavelength electrostatic waves in the presence of equilibrium density, temperature, magnetic field, and electrostatic potential gradients has been derived. New ion-temperature-gradient (ITG) driven drift-dissipative modes are shown to exist. An expression for anomalous ion energy transport caused by nonthermal electrostatic fluctuations is also derived. Furthermore, possible stationary solutions of the nonlinear system are obtained in the form of double vortex. On the other hand, the temporal behavior of newly derived nonlinear dissipative systems can be described by the generalized Lorenz–Stenflo equations which admit chaotic solutions. The results of the present investigation should be helpful for understanding the wave phenomena in space and tokamak plasmas.

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