Properties of a Periodic Ansatz for the Coarsening of Soliton-lattice

Accepté pour publication dans Journal of Discontinuity, Nonlinearity and Complexity.International audienceSoliton lattices are periodic solutions of Ginzburg-Landau equation which can be usefull tools to explore the coarsening process (or Ostwald ripening) which takes place during a Cahn-Hilliard dynamics. They can be used to identify the stationary solutions of the dynamics and how these intermediate states are destroyed by fluctuations. The coarsening process drives the systems from a stationary solution to the next one which is of period double and of lower energy. Using another family of soliton lattices, this process can be described continuously via a phase field equation. We present here properties of these two families, including the Fourier series decomposition of the non symetric soliton lattice which we use as building block of our ansatz