Regularity of the Scattering Matrix for Nonlinear Helmholtz Eigenfunctions

Jesse Gell-Redman, Andrew Hassell, Jacob Shapiro

We study the nonlinear Helmholtz equation $(\Delta -{\lambda }^2)u=\pm |u{|}^{p-1}u$ on ${\mathbb{R}}^n$, $\lambda >0$, $p\in \mathbb{N}$ odd, and more generally $({\Delta }_g+V-{\lambda }^2)u=N[u]$, where ${\Delta }_g$…