OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousRadialRiccati.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

The Riccati identity of the actual outgoing columns

No inverse derivative formula is assumed. Differentiate A Φ = Φ', then use invertibility of the two value columns to obtain the Riccati equation from their original second-order ODE.

  1. theorem OAI.DefocusingNLS.homogeneousTwoColumns_hasDerivAt line 21
  2. theorem OAI.DefocusingNLS.homogeneousValueInverse_differentiableAt line 31
  3. theorem OAI.DefocusingNLS.homogeneousTwoColumns_surjective line 47
  4. theorem OAI.DefocusingNLS.homogeneousRadialRiccati_from_columns line 53
  5. theorem OAI.DefocusingNLS.homogeneousRadialDefect_from_columns line 101