Oscillatory spatially periodic weakly nonlinear gravity waves on deep water

DOI10.1017/S0022112088001600zbMath0643.76017OpenAlexW2034416128MaRDI QIDQ3786102

Juan A. Zufiria

Publication date: 1988

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112088001600

zbMATH Keywords

stabilitytravelling wavesspatial spectrumweakly nonlinear Hamiltonian modelchaotic behaviour of water wavesexact water wave equationsspatially periodic wavetrains

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Partial differential equations of mathematical physics and other areas of application (35Q99) Basic methods in fluid mechanics (76M99)

Related Items (7)

Heteroclinic dynamics in a model of Faraday waves in a square container ⋮ Resonantly excited regular and chaotic motions in a rectangular wave tank ⋮ Orbits homoclinic to resonances, with an applications to chaos in a model of the forced and damped sine-Gordon equation ⋮ Appearance and disappearance of non-symmetric progressive capillary-gravity waves of deep water ⋮ Chaotic properties of internal wave triad interactions ⋮ The 1:2 resonance with \(O(2)\) symmetry and its applications in hydrodynamics ⋮ High-order formulation of the water-wave problem

Cites Work

• Universal behaviour in families of area-preserving maps
• Bifurcation at nonsemisimple 1:-1 resonance
• Homoclinic orbits in Hamiltonian systems
• Instability and confined chaos in a nonlinear dispersive wave system
• The superharmonic instability of finite-amplitude water waves
• Bifurcation in gravity waves
• The Superharmonic Instability of Finite-Amplitude Surface Waves on Water of Finite Depth
• Numerical Evidence for the Existence of New Types of Gravity Waves of Permanent Form on Deep Water
• Long wavelength bifurcation of gravity waves on deep water
• On the hamiltonian theory of surface waves
• The disintegration of wave trains on deep water Part 1. Theory

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