Scattering for a 3D coupled nonlinear Schrödinger system
Scattering for a 3D coupled nonlinear Schrödinger system
We consider a three-dimensional coupled cubic nonlinear Schrödinger system appearing in nonlinear optics. If (P, Q) is a ground state solution, we show that for any initial data (u0, v0) in H1(R3)×H1(R3) satisfying M(u0,v0)A(u0,v0)<M(P,Q)A(P,Q) and M(u0,v0)E(u0,v0)<M(P,Q)E(P,Q), where M(u, v) and E(u, v) are the mass and energy (invariant quantities) associated …