Oblique propagation of solitary and periodic nonlinear electrostatic waves in dusty plasmas

Analyses of the oblique propagation of large-amplitude electrostatic waves, encountered in the literature, make additional assumptions that the plasma response is quasi-neutral and that there is no more than one inertial fluid species, resulting in either a second-order differential equation or a Sagdeev-type energy integral. We revisit a simple model of a dusty plasma, with a cold negative dust component in the presence of hot Maxwellian positive ions, and assume for simplicity that all electrons have been accreted onto the dust grains. In going carefully through the mathematical framework, we pay particular attention to the intervening integrations, because we want a consistent picture covering both nonlinear solitary and periodic modes. The latter are often mistreated in the plasma literature for various models by neglecting the necessary conservation of species densities per cycle, lest one generate a nonphysical infinite overall gain or loss. We illustrate the different regimes by numerical examples and corresponding figures for the electrostatic wave potentials, Sagdeev pseudopotentials, electric fields, and conserved densities, as the case may be. This shows some familiarities, but a great variety in scales and wavelengths. The relevance of the theory in interpreting the waveforms of dust-acoustic waves in laboratory experiments and simulations is pointed out.