Breathing solitary waves in a Sine-Gordon two-dimensional lattice.

We study theoretically and numerically the dynamical behavior of a two-dimensional sine-Gordon lattice. We show that, via modulational instability, an initial-low-amplitude plane wave can evolve spontaneously into moving localized modes with large amplitude. These nonlinear modes, with dimensions depending on the characteristic wavelengths of the instability, behave like breathing solitary waves and present particlelike properties.