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We investigate the existence of normalized ground states to the system of coupled Schr\"odinger equations: equationeq: 0. 1 cases - u₁ + ₁ u₁ = ₁ |u₁|^p₁-2u₁ + r₁|u₁|^r₁-2u₁|u₂|^r₂ & in R^3, - u₂ + ₂ u₂ = ₂|u₂|^p₂-2u₂ + r₂|u₁|^r₁|u₂|^r₂-2u₂ & in R³, cases equation subject to the constraints S₀䃑 S₀䃒 = \ (u₁ H¹ (R³) ) |ₑ℃ u₁² dx = a₁²\ \ (u₂ H¹ (R³) ) |ₑ℃ u₂² dx = a₂²\, where ₁, ₂ > 0, r₁, r₂ > 1, and 0. Our focus is on the coupled mass super-critical case, specifically, 103. Furthermore, this result can be generalized to systems with an arbitrary number of components, and the corresponding standing wave is orbitally unstable.
Chengcheng Wu (Mon,) studied this question.