[PDF] Theory Of Nonlinear Lattices eBook

Author : Morikazu Toda
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 29,74 MB
Release : 2012-12-06
Category : Science
ISBN : 3642832199

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Soliton theory, the theory of nonlinear waves in lattices composed of particles interacting by nonlinear forces, is treated rigorously in this book. The presentation is coherent and self-contained, starting with pioneering work and extending to the most recent advances in the field. Special attention is focused on exact methods of solution of nonlinear problems and on the exact mathematical treatment of nonlinear lattice vibrations. This new edition updates the material to take account of important new advances.

Author : Morikazu Toda
Publisher : Springer
Page : 0 pages
File Size : 22,79 MB
Release : 1981
Category : Science
ISBN : 9783642965852

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This book deals with waves in lattices composed of particles interacting by nonlinear forces. Since motion in a lattice with exponential interac tion between nearest neighbors can be analyzed rigorously, it is treated as the central subject to be discussed. From the idea that the fundamentals of the mathematical methods for nonlinear lattices would be elucidated by rigorous results, I was led in 1966 to the lattice with exponential interaction, which has since proved to be a subject of intensive investigation by many researchers. Therefore I have tried to describe the development of the study of this lattice. The presentation is intended to be coherent and self-contained. Chapter 1 starts with a rather historical exposition, and deals with the motion in the lattices and in continuous systems in general. Funda mental concepts necessary for later chapters, including the partic1elike behavior of stable pulses (solitons), the most characteristic entities of the nonlinear waves, are introduced. The dual transformation, which exchanges the roles of particles and interaction, is described for devel opment in the next chapter.

Author : Morikazu Toda
Publisher : World Scientific
Page : 336 pages
File Size : 43,58 MB
Release : 1993
Category : Science
ISBN : 9789810214692

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This volume contains selected papers of Dr Morikazu Toda. The papers are arranged in chronological order of publishing dates. Among Dr Toda's many contributions, his works on liquids and nonlinear lattice dynamics should be mentioned. The one-dimensional lattice where nearest neighboring particles interact through an exponential potential is called the Toda lattice which is a miracle and indeed a jewel in theoretical physics. The papers in this volume can be grouped into five subjects: statistical mechanics, theory of liquids and solutions, lattice dynamics, Toda lattice and soliton theory and its applications.

Author : Fatkhulla Abdullaev
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 46,41 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401005427

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Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001

Author : K. Kaneko
Publisher :
Page : 208 pages
File Size : 36,35 MB
Release : 1993-04-13
Category : Mathematics
ISBN :

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The technique of the coupled map lattice (CML) is a rapidly developing field in nonlinear dynamics at present. This book gives a fully illustrative overview of current research in the field. A CML is a dynamical system in which there is some interaction ('coupled') between continuous state elements, which evolve in discrete time ('map') and are distributed on a discrete space ('lattice'). This book investigates both the theoretical aspects and applications of CMLs to spatially extended systems in nonlinear dynamical systems.

Author : Gerald Teschl
Publisher : American Mathematical Soc.
Page : 373 pages
File Size : 44,71 MB
Release : 2000
Category : Mathematics
ISBN : 0821819402

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This volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.

Author : Ignazio Licata and Sauro Succi
Publisher : MDPI
Page : 291 pages
File Size : 20,37 MB
Release : 2018-07-17
Category : Science
ISBN : 3038423068

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This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy

Author : Fatkhulla Abdullaev
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 36,78 MB
Release : 2002-01-31
Category : Mathematics
ISBN : 9781402001918

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Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001