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| Author | : Marek Antonowicz |
| Publisher | : |
| Total Pages | : 20 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
| Author | : Marek Antonowicz |
| Publisher | : |
| Total Pages | : 46 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
| Author | : Taixi Xu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
| Author | : Leonid A Dickey |
| Publisher | : World Scientific |
| Total Pages | : 421 |
| Release | : 2003-01-17 |
| Genre | : Science |
| ISBN | : 9814487422 |
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics.The second edition is up-to-date and differs from the first one considerably. One third of the book (five chapters) is completely new and the rest is refreshed and edited.
| Author | : Dickey Leonid A |
| Publisher | : World Scientific |
| Total Pages | : 320 |
| Release | : 1991-09-02 |
| Genre | : Science |
| ISBN | : 9813104341 |
The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Greene, Kruskal, and Miura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.This branch of science is attractive because it is one of those which revives the interest in the basic principles of mathematics, a beautiful formula.
| Author | : Maciej Blaszak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 355 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 364258893X |
This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system. As this property is closely related to integrability, this book presents an algebraic theory of integrable.
| Author | : P.R. Chernoff |
| Publisher | : Springer |
| Total Pages | : 165 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540372873 |
| Author | : Yuri B. Suris |
| Publisher | : Birkhäuser |
| Total Pages | : 1078 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034880162 |
An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.
| Author | : Sergej B. Kuksin |
| Publisher | : Springer |
| Total Pages | : 128 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540479201 |
The book is devoted to partial differential equations of Hamiltonian form, close to integrable equations. For such equations a KAM-like theorem is proved, stating that solutions of the unperturbed equation that are quasiperiodic in time mostly persist in the perturbed one. The theorem is applied to classical nonlinear PDE's with one-dimensional space variable such as the nonlinear string and nonlinear Schr|dinger equation andshow that the equations have "regular" (=time-quasiperiodic and time-periodic) solutions in rich supply. These results cannot be obtained by other techniques. The book will thus be of interest to mathematicians and physicists working with nonlinear PDE's. An extensivesummary of the results and of related topics is provided in the Introduction. All the nontraditional material used is discussed in the firstpart of the book and in five appendices.
| Author | : Maciej Błaszak |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 368 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : |
This book offers a modern introduction to the Hamiltonian theory of dynamical systems, presenting a unified treatment of all types of dynamical systems, i.e., finite, lattice, and field. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate system.
