Soliton solutions to systems of coupled Schrodinger equations of Hamiltonian type

Boyan Sirakov (1, 2) , Sérgio H.M. Soares (3)

1 MODAL'X - Modélisation aléatoire de Paris X
2 CAMS - Centre d'Analyse et de Mathématique sociales
3 Departamento de Matematica

We study existence of standing wave solutions of systems of coupled Schrodinger equations of Hamiltonian type. We prove that such solutions exist for small values of the parameter \hbar, provided the potential has a global well structure. We use Legendre-Fenchel transform, a mountain pass type argument, and Fourier analysis.

Domaines: Equations aux dérivées partielles [math.AP]

Boyan Sirakov, Sérgio H.M. Soares. Soliton solutions to systems of coupled Schrodinger equations of Hamiltonian type. Transactions of the American Mathematical Society, 2010, 362 (11), pp.5729-5744. ⟨hal-00178844v2⟩