Two families of vector solutions exist for the NLS system with weak three-wave coupling, approaching either all three or two scalar ground states as alpha goes to zero, but none approach a single nontrivial component.
Osada,Existence of a minimizer for a nonlinear Schr¨ odinger system with three wave interaction under non-symmetric potentials, Partial Differ
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On the existence of vector solutions to nonlinear Schr\"odinger equations with weak three-wave interaction
Two families of vector solutions exist for the NLS system with weak three-wave coupling, approaching either all three or two scalar ground states as alpha goes to zero, but none approach a single nontrivial component.