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.
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math.AP 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Global well-posedness holds for the Alber equation in H¹𝔖¹(𝕋) for non-negative self-adjoint data, with energy conservation and polynomial growth bounds on perturbations of stable backgrounds.
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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.
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Global solutions for the Alber equation in $H^1\mathfrak{S}^1(\mathbb{T})$
Global well-posedness holds for the Alber equation in H¹𝔖¹(𝕋) for non-negative self-adjoint data, with energy conservation and polynomial growth bounds on perturbations of stable backgrounds.