Klein-Gordon
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Euler-Korteweg vortices: A fluid-mechanical analogue to the Schr\"odinger and Klein-Gordon equations
arXiv:2512.23771v4 Announce Type: replace-cross Abstract: Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are mathematically equivalent to the Schr\"odinger and Klein-Gordon equations.
Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions
arXiv:2606.03407v1 Announce Type: cross Abstract: We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equations with mixed Dirichlet, Neumann, and periodic boundary conditions and source terms. While prior quantum algorithms usually neglect the stability problem from the PDE-to-ODE reduction, our method-of-lines approach investigates the boundary lifting via Coons...