article published yes Rowan Killip author Jason Murphy author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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. American Mathematical Society2023 eng 0002-9939 1088-6826 2207.0241410.1090/proc/16297 15162543-2557 yes Killip, Rowan, et al. “The Scattering Map Determines the Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 6, American Mathematical Society, 2023, pp. 2543–57, doi:<a href="https://doi.org/10.1090/proc/16297">10.1090/proc/16297</a>. Killip, R., Murphy, J., &#38; Vişan, M. (2023). The scattering map determines the nonlinearity. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/proc/16297">https://doi.org/10.1090/proc/16297</a> Killip R, Murphy J, Vişan M. 2023. The scattering map determines the nonlinearity. Proceedings of the American Mathematical Society. 151(6), 2543–2557. R. Killip, J. Murphy, and M. Vişan, “The scattering map determines the nonlinearity,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 6. American Mathematical Society, pp. 2543–2557, 2023. R. Killip, J. Murphy, M. Vişan, Proceedings of the American Mathematical Society 151 (2023) 2543–2557. Killip R, Murphy J, Vişan M. The scattering map determines the nonlinearity. <i>Proceedings of the American Mathematical Society</i>. 2023;151(6):2543-2557. doi:<a href="https://doi.org/10.1090/proc/16297">10.1090/proc/16297</a> Killip, Rowan, Jason Murphy, and Monica Vişan. “The Scattering Map Determines the Nonlinearity.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href="https://doi.org/10.1090/proc/16297">https://doi.org/10.1090/proc/16297</a>. 220642026-06-19T08:12:42Z2026-06-30T07:08:20Z