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1. The scattering map determines the nonlinearity

   https://doi.org/10.1090/proc/16297  

   Killip, Rowan; Murphy, Jason; Visan, Monica (March 2023, 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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2. MUSE: The MUon Scattering Experiment

   https://doi.org/10.21468/SciPostPhysProc.5.023  

   Cline, Ethan; Bernauer, Jan; Downie, Evangeline J.; Gilman, Ronald (January 2021, SciPost Physics Proceedings)

   MUSE is a high-precision muon scattering experiment aiming todetermine the proton radius. Muon, electron, and pion scattering will bemeasured at the same time. Two-photon exchange corrections will bedetermined with data using both beam polarities. 

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3. Scattering and inverse scattering for the AKNS system: A rational function approach

   https://doi.org/10.1111/sapm.12434  

   Trogdon, Thomas (August 2021, Studies in Applied Mathematics)

   Abstract We consider the use of rational basis functions to compute the scattering and inverse scattering transforms associated with the AKNS (Ablowitz–Kaup–Newell–Segur) system. The proposed numerical forward scattering transform computes the solution of the AKNS system that is valid on the entire real axis and thereby computes a reflection coefficient at a point by solving a single linear system. The proposed numerical inverse scattering transform makes use of a novel improvement in the rational function approach to the oscillatory Cauchy operator, enabling the efficient solution of certain Riemann–Hilbert problems without contour deformations. The latter development enables access to high‐precision computations and this is demonstrated on the inverse scattering transform for the one‐dimensional Schrödinger operator with a potential. 

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4. Spatial effects of HF multiple scattering in the ionosphere: Experimental observations: MULTIPLE SCATTERING IN THE IONOSPHERE

   https://doi.org/10.1029/2011RS004645  

   Zabotin, Nikolay; Bullett, Terence (August 2011, Radio Science)
5. Electroweak scattering at the muon shot

   https://doi.org/10.1103/PhysRevD.110.013005  

   Han, Tao; Liu, Da; Low, Ian; Wang, Xing (July 2024, Physical Review D)

   It has long been recognized that the scattering of electroweak particles at very high energies is dominated by vector boson fusion, which probes the origin of electroweak symmetry breaking and offers a unique window into the ultraviolet regime of the Standard Model (SM). Previous studies assume SM-like couplings and rely on the effective $W$approximation (or electroweak parton distribution), whose validity is well established within the SM but not yet studied in the presence of anomalous Higgs couplings. In this work, we critically examine the electroweak production of two Higgs bosons in the presence of anomalous $VVh$and $VVhh$couplings. We compute the corresponding helicity amplitudes and compare the cross section results in the effective $W$approximation with the full fixed-order calculation. In particular, we identify two distinct classes of anomalous Higgs couplings, whose effects are not captured by vector boson fusion and effective $W$approximation. Such very-high-energy electroweak scatterings can be probed at the muon shot, a multi-TeV muon collider upon which we base our study, although similar considerations apply to other high-energy colliders. Published by the American Physical Society2024 

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