Solutions to linear and nonlinear Schrödinger equations in 2D and 3D can be constructed with prescribed, arbitrarily large and highly localized spatial gradients near chosen boundary points.
Loh¨ ormander, Inequalities for the associated Legendre functions,Journal of Approximation Theory, 95(2) (1998), 178–193
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Construction of Solutions with Extraordinary Gradient Amplification and Localization for Schr\"odinger Equations
Solutions to linear and nonlinear Schrödinger equations in 2D and 3D can be constructed with prescribed, arbitrarily large and highly localized spatial gradients near chosen boundary points.