Periodic Gravity-Capillary Wave
A periodic traveling wave driven simultaneously by gravity and surface tension. Its governing equations include nonlinear terms and higher-order dispersion terms, and classical perturbation theory often fails in the high-amplitude regime.
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This research proposes a computational framework that combines machine learning discovery with computer-assisted numerical certification and formal verification, achieving near-machine-precision residuals for periodic gravity-capillary waves.
Periodic gravity-capillary waves are periodic traveling waves driven simultaneously by gravity and surface tension; their governing equations contain nonlinear terms and higher-order dispersive terms, surface tension causes the wave speed to vary non-monotonically with amplitude, classical perturbation theory fails in the high-amplitude regime, and curvature singularities at wave crests (Wilton ripples) even appear.
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This research proposes a computational framework that combines machine learning discovery with computer-assisted numerical certification and formal verification, achieving near-machine-precision residuals for periodic gravity-capillary waves.
50%UnverifiedPeriodic gravity-capillary waves are periodic traveling waves driven simultaneously by gravity and surface tension; their governing equations contain nonlinear terms and higher-order dispersive terms, surface tension causes the wave speed to vary non-monotonically with amplitude, classical perturbation theory fails in the high-amplitude regime, and curvature singularities at wave crests (Wilton ripples) even appear.
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