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Creators/Authors contains: "Visan, Monica"

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  1. ; ; (, 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
  2. ; ; ; (, Discrete and Continuous Dynamical Systems)
    Free, publicly-accessible full text available January 1, 2026
  3. ; ; ; (, 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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  4. ; ; (, 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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  5. ; ; (, Annals of PDE)
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  6. ; ; (, SIAM Journal on Mathematical Analysis)
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  7. ; ; (, Inventiones mathematicae)
    null (Ed.)
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  8. ; ; (, SIAM Journal on Mathematical Analysis)
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  9. ; (, RIMS kokyuroku bessatsu)
    We present two adaptations of an argument of Sonin, which is known to be a powerful tool for obtaining both qualitative and quantitative information about special functions; see [12]. Our particular applications are as follows: (i) We give a rigorous formulation and proof of the following assertion about focusing NLS in any dimension: The spatial envelope of aspherically symmetric soliton in arepulsive potential is a non‐increasing function of the radius. (ii) Driven by the question of determining the most stably singular matrix, we determine the location of the maximal eigenvalue density of an ncross n GUE matrix. Strikingly, in even dimensions, this maximum is not at zero. 
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    Accepted Manuscript Full Text Available