A Schr”odinger-Based Dispersive Regularization Approach for Numerical Simulation of One-Dimensional Shallow Water Equations
arXiv:2601.02561v1 Announce Type: new Abstract: We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum equation, which renders the system equivalent, via the Madelung transform, to a defocusing cubic nonlinear Schr”odinger equation with a drift term induced by bottom topography. Instead of solving the shallow water equations directly, we solve the associated Schr”odinger equation and recover […]