Affiliations: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale A. Moro 5, I-00185 Roma, Italy. E-mail: [email protected] | Dipartimento di Scienze Applicate, Università degli Studi di Napoli “Parthenope”, CDN Isola C4, I-80143 Napoli, Italy. E-mail: [email protected] | Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, I-37134 Verona, Italy. E-mail: [email protected]
Abstract: The semiclassical limit of a weakly coupled nonlinear focusing Schrödinger system in presence of a nonconstant potential is studied. The initial data is of the form (u1, u2) with ui=ri ((x−x˜)/ε)e(i/ε)x·ξ˜, where (r1, r2) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For ε sufficiently small, the solution (ϕ1, ϕ2) will been shown to have, locally in time, the form (r1 ((x−x(t))/ε)e(i/ε)x·ξ(t), r2 ((x−x(t))/ε)e(i/ε)x·ξ(t)), where (x(t), ξ(t)) is the solution of the Hamiltonian system x˙(t)=ξ(t), ξ˙(t)=−∇V(x(t)) with x(0)=x˜ and ξ(0)=ξ˜.
Keywords: weakly coupled nonlinear Schrödinger systems, concentration phenomena, semiclassical limit, orbital stability of ground states, soliton dynamics
