Ion-acoustic shocks in space and laboratory dusty plasmas: Two-dimensional and non-traveling-wave observable effects

Some recent observations of the ion-acoustic shocks in dusty plasmas have been explained via the one-dimensional Korteweg–de Vries–Burgers equation (1-D-KdVB). To help study the space and laboratory plasma systems, the investigation on a two-dimensional generalization of the 1-D-KdVB is performed with computerized symbolic computation. An auto-Bäcklund transformation and some monotonic-shock-wave-like, exact analytic solutions are found. Then, several observable effects are predicted, which the future space and laboratory plasma experiments might discover, beyond the existing one-dimensional and traveling-wave considerations.