 Schrödinger trapped defocusing stationary equation

ID: schrodinger-trapped-defocusing-stationary-equation

Critical points of the trapped defocusing cubic energy

J (v) = \frac{1}{2} ∥ v ∥_{Σ}^{2} - \frac{ω}{2} ∥ v ∥_{2}^{2} + \frac{1}{4} ∥ v ∥_{4}^{4}

satisfy

- Δ v + ∣ x ∣^{2} v - ω v + v^{3} = 0

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