On the periodic solutions of a forced second-order equation
type: Item
instance of: scholarly article
title: On the periodic solutions of a forced second-order equation
zbMATH Open document ID: 0801.34040
DOI: 10.1007/BF01209067
published in: Journal of Nonlinear Science
publication date: 1994-11-30T00:00:00Z
review text: A two-dimensional irrotational forced shallow water sloshing model leads in the case of periodic solutions to a second-order nonlinear nonautonomous ordinary differential equation. Shooting technique resembling that used previously for the Falkner-Skan equation is applied. The existence of many harmonic and subharmonic solutions is rigorously proved confirming previously found (4th order Runge-Kutta) numerical solutions. A ``Kneading'' theory is obtained for the ordering of the initial conditions according to the pattern of ``spikes'' exhibited by the solution.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 65J99
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 563418
zbMATH Keywords: homoclinic chaos
zbMATH Keywords: shooting technique
zbMATH Keywords: kneading
zbMATH Keywords: spikes
zbMATH Keywords: two-dimensional irrotational forced shallow water sloshing model
zbMATH Keywords: periodic solutions
zbMATH Keywords: second-order nonlinear nonautonomous ordinary differential equation
zbMATH Keywords: Falkner-Skan equation
zbMATH Keywords: harmonic and subharmonic solutions
author: S. P. Hastings
author: J. B. McLeod
reviewed by: Maria Gousidou-Koutita
MaRDI profile type: Publication
cites work: Resonant oscillations in shallow water with small mean-square disturbances
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Oscillating solutions of the Falkner-Skan for positive \(\beta\)
cites work: Resonant sloshing in shallow water
cites work: Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
cites work: 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
full work available at URL: https://doi.org/10.1007/bf01209067
OpenAlex ID: W2086531191
description: scientific article; zbMATH DE number 563418