Journal ArticleDOI
Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation
Gregor Kovačič,Stephan Wiggins +1 more
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TLDR
In this article, the authors developed new global perturbation techniques for detecting homoclinic trajectories in a class of four dimensional ordinary differential equations that are perturbations of completely integrable two-degree-of-freedom Hamiltonian systems.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1992-06-15. It has received 199 citations till now. The article focuses on the topics: Heteroclinic orbit & Homoclinic orbit.read more
Citations
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Morse and Melnikov functions for NLS Pde's
Yanyan Li,David W. McLaughlin +1 more
TL;DR: The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat linear operator, is developed in sufficient detail for later use in studies of perturbations of NLS equations as mentioned in this paper.
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Non-linear dynamics of a shallow arch under periodic excitation. II: 1:1 Internal resonance
TL;DR: In this paper, Tien et al. studied the dynamics of a shallow arch subjected to harmonic excitation in the presence of both external and 1:1 internal resonance, and the method of averaging was used to yield a set of autonomous equations of the second-order approximations to the response of the system.
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Persistent homoclinic orbits for a perturbed nonlinear schrodinger equation
TL;DR: In this article, the existence of a symmetric pair of homoclinic orbits for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE is established.
Journal ArticleDOI
Global and chaotic dynamics for a parametrically excited thin plate
TL;DR: In this article, the global bifurcations and chaotic dynamics of a parametrically excited, simply supported rectangular thin plate are analyzed using the von Karman-type equation and Galerkin's approach.
References
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Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
Journal ArticleDOI
Geometric singular perturbation theory for ordinary differential equations
Journal ArticleDOI
The dynamics of coherent structures in the wall region of a turbulent boundary layer.
TL;DR: In this article, the wall region of a turbulent boundary layer is modelled by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem.
Book
Solitons in mathematics and physics
TL;DR: The history of the Soliton derivation of the Korteweg-de Vries, nonlinear Schrodinger and other important and Canonical Equations of Mathematical Physics Soliton Equation families and Solution Methods The -Function, the Hirota Method, the Painleve Property and Backlund Transformations for the KORTewegde Vrie Family of Soliton Eq.
Book
Global Bifurcations and Chaos: Analytical Methods
TL;DR: Global Bifurcations and Chaos: Analytical Methods as discussed by the authors describes the mechanisms which give rise to chaos and derives explicit techniques whereby these mechanisms can be detected in specific systems.