Soliton-stripe patterns of a functional with an attractive-repulsive-attractive interaction

We study critical points of a Ginzburg-Landau type functional with an attractive-repulsive-attractive nonlocal interaction. Using an appropriate scaling and the Γ-convergence method we reduce the problem to a finite dimensional one. In contrast to a similar problem with just an attractive-repulsive interaction, we obtain a richer set of solutions. The soliton-stripe patterns appear as skewed local minimizers of the free energy, and dissappear or become symmetric as the number of interfaces reaches a certain threshold. We also show how other critical points can be constructed using results of the diblock copolymer problem.