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Discontinuity, Nonlinearity, and Complexity 3(1) (2014) 73--86 | DOI:10.5890/DNC.2014.03.006

Simon Villain-Guillot

Laboratoire Onde et Matière d’Aquitaine, Université de Bordeaux, 351 cours de la Libéation 33405 Talence Cedex, France

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Abstract

Soliton lattices are periodic solutions of Ginzburg-Landau equation which can be useful 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 intermedi- ate 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 symmetric soliton lattice which we use as building block of our ansatz.

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