Nonlinear Waves in Integrable and Nonintegrable Systems PDF Download
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Author: Jianke Yang
Publisher: SIAM
ISBN: 0898719682
Category : Science
Languages : en
Pages : 453
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Book Description
Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.
Author: Jianke Yang
Publisher: SIAM
ISBN: 0898719682
Category : Science
Languages : en
Pages : 453
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Book Description
Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.
Author: Lokenath Debnath
Publisher: CUP Archive
ISBN: 9780521254687
Category : Mathematics
Languages : en
Pages : 376
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Book Description
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Author: Katelyn Plaisier Leisman
Publisher:
ISBN:
Category :
Languages : en
Pages : 548
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Book Description
Author: Gérard A. Maugin
Publisher:
ISBN: 9780198534846
Category : Mathematics
Languages : en
Pages : 328
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Book Description
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
Author: Lokenath Debnath
Publisher: Cambridge University Press
ISBN: 0511868618
Category : Mathematics
Languages : en
Pages : 372
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Book Description
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Author: Christopher W. Curtis
Publisher:
ISBN: 9781470422745
Category : Nonlinear wave equations
Languages : en
Pages :
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Book Description
Author: Lokenath Debnath
Publisher: World Scientific
ISBN: 9814554960
Category :
Languages : en
Pages : 683
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Book Description
This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.
Author: Elena Tobisch
Publisher: Springer
ISBN: 3319206907
Category : Science
Languages : en
Pages : 309
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Book Description
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.
Author: Decio Levi
Publisher: American Mathematical Society, Centre de Recherches Mathématiques
ISBN: 0821843540
Category : Mathematics
Languages : en
Pages : 520
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Book Description
This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.
Author: Morikazu Toda
Publisher: Springer Science & Business Media
ISBN: 3642832199
Category : Science
Languages : en
Pages : 233
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Book Description
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.
