A hyperbolic relaxation of the nonlinear Schrödinger equation conserves three analogs of NLS invariants and admits standing-wave solutions that converge linearly to NLS ground states as the relaxation parameter vanishes.
Perfectly matched layers methods for mixed hyperbolic–dispersive equations.Water Waves, 4(3):313–343, 2022
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A Hyperbolic Approximation of the Nonlinear Schr\"odinger Equation
A hyperbolic relaxation of the nonlinear Schrödinger equation conserves three analogs of NLS invariants and admits standing-wave solutions that converge linearly to NLS ground states as the relaxation parameter vanishes.