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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.
Book Synopsis Theory of Nonlinear Lattices by : Morikazu Toda
Download or read book Theory of Nonlinear Lattices written by Morikazu Toda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Theory of Nonlinear Lattices by : Morikazu Toda
Download or read book Theory of Nonlinear Lattices written by Morikazu Toda and published by Springer. This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Nonlinear Lattices Nonlinear Lattices by : Morikazu Toda
Download or read book Theory of Nonlinear Lattices Nonlinear Lattices written by Morikazu Toda and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Nonlinear Lattices (Volume 20 of Springer Series in Solid-State Sciences). by : M. Toda
Download or read book Theory of Nonlinear Lattices (Volume 20 of Springer Series in Solid-State Sciences). written by M. Toda and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Theory and Applications of Coupled Map Lattices by : K. Kaneko
Download or read book Theory and Applications of Coupled Map Lattices written by K. Kaneko and published by . This book was released on 1993-04-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Jacobi Operators and Completely Integrable Nonlinear Lattices by : Gerald Teschl
Download or read book Jacobi Operators and Completely Integrable Nonlinear Lattices written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2000 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
Book Synopsis Nonlinearity and Disorder: Theory and Applications by : Fatkhulla Abdullaev
Download or read book Nonlinearity and Disorder: Theory and Applications written by Fatkhulla Abdullaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
Book Synopsis Dynamics of Lattice Materials by : A. Srikantha Phani
Download or read book Dynamics of Lattice Materials written by A. Srikantha Phani and published by John Wiley & Sons. This book was released on 2017-09-25 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Offers comprehensive treatment of dynamics of lattice materials and periodic materials in general, including phononic crystals and elastic metamaterials Provides an in depth introduction to elastostatics and elastodynamics of lattice materials Covers advanced topics such as damping, nonlinearity, instability, impact and nanoscale systems Introduces contemporary concepts including pentamodes, local resonance and inertial amplification Includes chapters on fast computation and design optimization tools Topics are introduced using simple systems and generalized to more complex structures with a focus on dispersion characteristics
This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy
Book Synopsis Non-Linear Lattice by : Ignazio Licata and Sauro Succi
Download or read book Non-Linear Lattice written by Ignazio Licata and Sauro Succi and published by MDPI. This book was released on 2018-07-17 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy
Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
Book Synopsis Nonlinearity and Disorder: Theory and Applications by : Fatkhulla Abdullaev
Download or read book Nonlinearity and Disorder: Theory and Applications written by Fatkhulla Abdullaev and published by Springer Science & Business Media. This book was released on 2002-01-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001
