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Creators/Authors contains: "Killip, Rowan"

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  1. ; ; (, Pure and Applied Analysis)
    Free, publicly-accessible full text available January 1, 2026
  2. ; ; (, Nonlinearity)
    Abstract We prove that the small-data scattering map uniquely determines the nonlinearity for a wide class of gauge-invariant, intercritical nonlinear Schrödinger equations. We use the Born approximation to reduce the analysis to a deconvolution problem involving the distribution function for linear Schrödinger solutions. We then solve this deconvolution problem using the Beurling–Lax Theorem. 
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    Free, publicly-accessible full text available December 30, 2025
  3. ; ; ; (, Discrete and Continuous Dynamical Systems)
    Free, publicly-accessible full text available January 1, 2026
  4. ; ; (, Inventiones mathematicae)
    Full Text Available 
  5. ; ; ; (, Journal of the European Mathematical Society)
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  6. ; ; (, Duke Mathematical Journal)
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  7. ; ; ; (, Nonlinearity)
    Abstract We show that solutions to the Ablowitz–Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely L 2 initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations. 
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  8. ; ; (, Proceedings of the American Mathematical Society)
    Using the two-dimensional nonlinear Schrödinger equation as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild assumptions on the nonlinearity, the wave operator uniquely determines the nonlinearity, as does the scattering map. Evaluating the scattering map on well-chosen initial data, we reduce the problem to an inverse convolution problem, which we solve by means of an application of the Beurling–Lax Theorem. 
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  9. ; ; (, Analysis & PDE)
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  10. ; (, Communications in Mathematical Physics)
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