For small prescribed masses, the m-coupled Gross-Pitaevskii system on a bounded domain in R^3 or R^4 admits arbitrarily many sign-changing and semi-nodal normalized solutions, for all signs of the coupling constants.
Bartsch, Bifurcation in a multicomponent system of nonlinear Schr¨odinger equations, J
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Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domains: the $L^2$-supercritical case
For small prescribed masses, the m-coupled Gross-Pitaevskii system on a bounded domain in R^3 or R^4 admits arbitrarily many sign-changing and semi-nodal normalized solutions, for all signs of the coupling constants.