On the periodic solutions of a forced second-order equation

DOI10.1007/BF01209067zbMath0801.34040OpenAlexW2086531191MaRDI QIDQ1322678

Stuart P. Hastings, John Bryce McLeod

Publication date: 30 November 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01209067

zbMATH Keywords

spikesperiodic solutionsshooting techniqueFalkner-Skan equationhomoclinic chaoskneadingharmonic and subharmonic solutionssecond-order nonlinear nonautonomous ordinary differential equationtwo-dimensional irrotational forced shallow water sloshing model

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Numerical analysis in abstract spaces (65J99)

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Cites Work

• Oscillating solutions of the Falkner-Skan for positive \(\beta\)
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• Resonant sloshing in shallow water
• Resonant oscillations in shallow water with small mean-square disturbances
• On the Detection and Dynamical Consequences of Orbits Homoclinic to Hyperbolic Periodic Orbits and Normally Hyperbolic Invariant Tori in a Class of Ordinary Differential Equations