Characterization of Pattern Formation from Modulation Instability in the Cubic Schrodinger Equation

The study of pattern dynamics in a Hamiltonian system(HS) having an infinite number of degree of freedom is very difficult due to the absence of attractors in such system. In this letter, we propose a useful method that only a few representative manifolds in phase space are investigated, and it can be used to reveal the pattern formation of HS. The conserved cubic Schrödinger equation is discussed. Although a special model is chosen, this method can be applied to more general case such as the near-integrable HS.