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A generalized hydrodynamic (GHD) model depicting the behaviour of visco-elastic fluids has often been invoked to explore the behaviour of a strongly coupled dusty plasma medium below their crystallization limit. The model has been successful in describing the collective normal modes of the strongly coupled dusty plasma medium observed experimentally. The paper focuses on the study of nonlinear dynamical characteristic features of this model. Specifically, the evolution of coherent vorticity patches are being investigated here within the framework of this model. A comparison with Newtonian fluids and Molecular Dynamics (MD) simulations treating the dust species interacting through the Yukawa potential has also been presented.

The experimentally measured waveform of nonlinear dust acoustic waves in a plasma is shown, by analyzing experimental data, to be accurately described by a cnoidal function. This function, which is predicted by nonlinear theory, has broad minima and narrow peaks, and we found that the waveforms in the experimental data match. Fitting the experimental waveforms to the cnoidal function also provides a measure of the wave's nonlinearity, namely, the elliptical parameter k. By characterizing experimental results at various wave amplitudes, we confirm that the parameter k varies upwardincreases and approaches a maximum value of unity, as the wave amplitude is increased. The underlying theory that predicts the cnoidal waveform as an exact solution of a Korteweg-de Vries model equation takes account of the streaming ions that are responsible for the spontaneous excitation of the dust acoustic waves.

The nonlinear propagation of low-frequency waves in a strongly coupled dusty plasma medium is studied theoretically in the framework of the phenomenological generalized hydrodynamic (GH) model. A set of simplified model nonlinear equations are derived from the original nonlinear integrodifferential form of the GH model by employing an appropriate physical ansatz. Using standard perturbation techniques characteristic evolution equations for finite small amplitude waves are then obtained in various propagation regimes. The influence of viscoelastic properties arising from dust correlation contributions on the nature of nonlinear solutions is discussed. The modulational stability of dust acoustic waves to parallel perturbation is also examined and it is shown that dust compressibility contributions influenced by the Coulomb coupling effects introduce significant modification in the threshold and range of the instability domain.

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