OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousGeneratorPerturbation.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

The generator identity for the constructed linearized flow

This derives the bounded-potential perturbation identity from the actual finite-slab Duhamel construction. No generator-domain assumption is added.

  1. def OAI.DefocusingNLS.homogeneousLinearizedHistory line 28
  2. theorem OAI.DefocusingNLS.continuous_homogeneousLinearizedHistory line 31
  3. theorem OAI.DefocusingNLS.homogeneousLinearizedHistory_zero line 37
  4. theorem OAI.DefocusingNLS.homogeneousLinearizedStep_duhamel line 42
  5. theorem OAI.DefocusingNLS.homogeneousFree_derivWithin_of_linearized line 71

    Source documentation

    Every strong right derivative of the actual flow identifies the free generator after subtracting the actual linearized potential.

    theorem homogeneousFree_derivWithin_of_linearized (u v : HomogeneousY a k)
    (hu : HasDerivWithinAt (fun t : ℝ => S t.toNNReal u) v (Ici 0) 0) :
    HasDerivWithinAt (fun t : ℝ => homogeneousFreeOperator a b k t ha ha1 hk u)
      (v - B u) (Ici 0) 0 := by
…

    Mentions: OAI.DefocusingNLS.HomogeneousY, OAI.DefocusingNLS.homogeneousFreeOperator