A Simple Model for Spatio-Temporal Chaos in an Unstable Burgers Equation

We consider an unstable Burgers equation that exhibits spatio-temporal chaos. This spatio-temporal chaos is characterized by creation and merging processes of shock structures. We attempt to construct a simple model for the dynamics of these shocks. We also study a two-dimensional unstable Burgers equation. §1. Introduction and an unstable Burgers equation Pattern formation and nonlinear dynamics have been investigated in many spa-tially extended dissipative systems. 1), 2) Spatio-temporal chaos has been studied as a typical dynamical state far from equilibrium. Many model equations that can exhibit spatio-temporal chaos have been proposed. The Kuramoto-Sivashinsky equation i