Solutions on a torus for a semilinear equation

Genevieve Allain (1) , Anne Beaulieu (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We are interested in the positive doubly periodic solutions, which are even in each variable, of a stationary nonlinear Schrödinger equation in ℝ2, with a small parameter. For any pair of periods (2a, 2b), we construct a branch of solutions that concentrate uniformly to the ground-state solution of the equation.

Domaines: Equations aux dérivées partielles [math.AP]

Genevieve Allain, Anne Beaulieu. Solutions on a torus for a semilinear equation. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2011, 141 (2), pp.371-382. ⟨10.1017/S0308210509001772⟩. ⟨hal-00727772⟩