(untitled) (Journal of Nonlinear Modeling and Analysis, 2026)
This paper studies the cubic nonlinear Schrödinger system with partial confinement: cases-iφ_t + (x_1^2 + x_2^2)φ = Δφ +μ_1|φ|^2φ + β|ψ|^2φ, & (t,x) R^+× R^3, -iψ_t + (x_1^2 + x_2^2)ψ =Δψ + μ_2|ψ|^2ψ + β|φ|^2ψ, & (t,x) R^+ × R^3,cases which models the Bose-Einstein condensates with multiple states or the propagation of mutually incoherent wave packets in nonlinear optics. The cross-invariant sets of the evolution flow are obtained by constructing the cross-constrained variational problem. Furthermore, the sharp condition for global existence and blowup of the solutions is derived.