Stability of traveling water waves on the sphere

DOI10.1016/S0378-4754(00)00289-5zbMath1031.76019MaRDI QIDQ5937548

Panayotis Panayotaros

Publication date: 12 July 2001

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

zbMATH Keywords

spherical harmonicperiodic orbitsHamiltonian systemsnormal formsfree surface potential flowGalerkin truncationsgravitating spherelong-time nonlinear stabilityresonantly coupled harmonic oscillatorsStokes wavesweakly nonlinear water waves

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Nonlinear effects in hydrodynamic stability (76E30) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Interfacial stability and instability in hydrodynamic stability (76E17)

Cites Work

• Unnamed Item
• Composition of Lie transforms with rigorous estimates and applications to Hamiltonian perturbation theory
• The modulational regime of three-dimensional water waves and the Davey-Stewartson system
• Hamiltonian long-wave approximations to the water-wave problem
• Near-monochromatic water waves on the sphere
• Gravity waves on the surface of the sphere
• Existence of nonlinear normal modes of symmetric Hamiltonian systems
• Lie series and invariant functions for analytic symplectic maps
• Nonlinear stability around an elliptic equilibrium point in a Hamiltonian system
• The disintegration of wave trains on deep water Part 1. Theory

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