Korea Advance Institute of Science and Technology
Non-equilibrium process in pattern selection
When the question “Is the solar system stable?” was first raised by King Oscar II, Poincaré realized that the question ultimately led us to the fundamental mathematical question “Is a periodic orbit stable?”“How a periodic orbit or state loses its stability in a continuous medium?” As a play ground, we consider the Stokes wave, an homogeneous periodic state that appears generically in weakly nonlinear dispersive media, and analyze the non-equilibrium process of pattern formation/selection taking place beyond the threshold of instability. We consider the situation of Hamiltonian limit as well as the situation under dissipation. In both cases we analyze topologically completely the non-equilibrium process associated with patterns, which therefore bears certain generic significance.