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Articles 1 - 5 of 5
Full-Text Articles in Non-linear Dynamics
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
Theses, Dissertations and Capstones
The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …
Poisson Structure And Action-Angle Variables For The Camassa-Holm Equation, Adrian Constantin, Rossen Ivanov
Poisson Structure And Action-Angle Variables For The Camassa-Holm Equation, Adrian Constantin, Rossen Ivanov
Articles
The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.
Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov
Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov
Articles
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.
Hamiltonian Formulation And Integrability Of A Complex Symmetric Nonlinear System, Rossen Ivanov
Hamiltonian Formulation And Integrability Of A Complex Symmetric Nonlinear System, Rossen Ivanov
Articles
The integrability of a complex generalisation of the ’elegant’ system, proposed by D. Fairlie and its relation to the Nahm equation and the Manakov top is discussed.
Extended Camassa-Holm Hierarchy And Conserved Quantities, Rossen Ivanov
Extended Camassa-Holm Hierarchy And Conserved Quantities, Rossen Ivanov
Articles
An extension of the Camassa-Holm hierarchy is constructed in this letter. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived.