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.
Approximation of arbitrarily high-order PDEs by first-order hyperbolic relaxation.Nonlinearity, 38(5):055002, 2025
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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.