Initial-value problems are investigated numerically for a two-dimensional (2D) nonlinear long-wavelength equation including effects of instability, dissipation, and dispersion. It is found that one-dimensional structures are always unstable and localized 2D structures are generated. For relatively weak dispersion, the localized structures are not distinct and the overall evolutions are irregular. For strongly dispersive cases, a number of bell-shaped pulses of equal amplitude exist stably in the time asymptotic state and they form a quasistationary lattice for certain initial conditions.

• Received 17 April 1989

DOI:https://doi.org/10.1103/PhysRevA.40.5472