Discrete Systems and Integrability

Author: J. Hietarinta
Publisher: Cambridge University Press
ISBN: 1107042720
Format: PDF, Mobi
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A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Isochronous Systems

Author: Francesco Calogero
Publisher: OUP Oxford
ISBN: 0191538655
Format: PDF
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A dynamical system is called isochronous if it features in its phase space an open, fully-dimensional region where all its solutions are periodic in all its degrees of freedom with the same, fixed period. Recently a simple transformation has been introduced, applicable to quite a large class of dynamical systems, that yields autonomous systems which are isochronous. This justifies the notion that isochronous systems are not rare. In this book the procedure to manufacture isochronous systems is reviewed, and many examples of such systems are provided. Examples include many-body problems characterized by Newtonian equations of motion in spaces of one or more dimensions, Hamiltonian systems, and also nonlinear evolution equations (PDEs). The book shall be of interest to students and researchers working on dynamical systems, including integrable and nonintegrable models, with a finite or infinite number of degrees of freedom. It might be used as a basic textbook, or as backup material for an undergraduate or graduate course.

Integrals of Nonlinear Equations of Evolution and Solitary Waves Classic Reprint

Author: Peter D. Lax
ISBN: 9781332144877
Format: PDF, Mobi
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Excerpt from Integrals of Nonlinear Equations of Evolution and Solitary Waves In section 1 we present a general principle for associating nonlinear equations of evolutions with linear operators so that the eigenvalues of the linear operator are integrals of the nonlinear equation. A striking instance of such a procedure is the discovery by Gardner, Miura and Kruskal that the eigenvalues of the Schrodinger operator are integrals of the Korteweg-de Vries equation. In section 2 we prove the simplest case of a conjecture of Kruskal and Zabusky concerning the existence of double wave solutions of the Korteweg-de Vries equation, i.e. of solutions which for -t- large behave as the superposition of two solitary waves travelling at different speeds The main tool used is the first of a remarkable series of integrals discovered by Kruskal and Zabusky. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.