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Nonlinear Wave Dynamics

Author: J. Engelbrecht

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 197

ISBN-13: 9401588910

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At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Book Synopsis Nonlinear Wave Dynamics by : J. Engelbrecht

Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Linear and Nonlinear Waves

Author: G. B. Whitham

Publisher: John Wiley & Sons

Published: 2011-10-18

Total Pages: 660

ISBN-13: 1118031202

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Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Book Synopsis Linear and Nonlinear Waves by : G. B. Whitham

Download or read book Linear and Nonlinear Waves written by G. B. Whitham and published by John Wiley & Sons. This book was released on 2011-10-18 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.

Nonlinear Waves, Solitons and Chaos

Author: Eryk Infeld

Publisher: Cambridge University Press

Published: 2000-07-13

Total Pages: 416

ISBN-13: 9780521635578

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The second edition of a highly successful book on nonlinear waves, solitons and chaos.

Book Synopsis Nonlinear Waves, Solitons and Chaos by : Eryk Infeld

Download or read book Nonlinear Waves, Solitons and Chaos written by Eryk Infeld and published by Cambridge University Press. This book was released on 2000-07-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a highly successful book on nonlinear waves, solitons and chaos.

Nonlinear Optical Waves

Author: A.I. Maimistov

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 668

ISBN-13: 9401724482

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A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.

Book Synopsis Nonlinear Optical Waves by : A.I. Maimistov

Download or read book Nonlinear Optical Waves written by A.I. Maimistov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.

Dynamical Systems and Nonlinear Waves in Plasmas

Author: Santo Banerjee

Publisher: CRC Press

Published: 2021-09-10

Total Pages: 218

ISBN-13: 1000404757

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Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Book Synopsis Dynamical Systems and Nonlinear Waves in Plasmas by : Santo Banerjee

Download or read book Dynamical Systems and Nonlinear Waves in Plasmas written by Santo Banerjee and published by CRC Press. This book was released on 2021-09-10 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems and Nonlinear Waves in Plasmas is written in a clear and comprehensible style to serve as a compact volume for advanced postgraduate students and researchers working in the areas of Applied Physics, Applied Mathematics, Dynamical Systems, Nonlinear waves in Plasmas or other nonlinear media. It provides an introduction to the background of dynamical systems, waves, oscillations and plasmas. Basic concepts of dynamical systems and phase plane analysis for the study of dynamical properties of nonlinear waves in plasmas are presented. Different kinds of waves in plasmas are introduced. Reductive perturbative technique and its applications to derive different kinds of nonlinear evolution equations in plasmas are discussed. Analytical wave solutions of these nonlinear evolution equations are presented using the concept of bifurcation theory of planar dynamical systems in a very simple way. Bifurcations of both small and arbitrary amplitudes of various nonlinear acoustic waves in plasmas are presented using phase plots and time-series plots. Super nonlinear waves and its bifurcation behaviour are discussed for various plasma systems. Multiperiodic, quasiperiodic and chaotic motions of nonlinear plasma waves are discussed in presence of external periodic force. Multistability of plasma waves is investigated. Stable oscillation of plasma waves is also presented in dissipative plasmas. The book is meant for undergraduate and postgraduate students studying plasma physics. It will also serve a reference to the researchers, scientists and faculties to pursue the dynamics of nonlinear waves and its properties in plasmas. It describes the concept of dynamical systems and is useful in understanding exciting features, such as solitary wave, periodic wave, supernonlinear wave, chaotic, quasiperiodic and coexisting structures of nonlinear waves in plasmas. The concepts and approaches, discussed in the book, will also help the students and professionals to study such features in other nonlinear media.

Nonlinear Oscillations and Waves in Dynamical Systems

Author: P.S Landa

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 550

ISBN-13: 9401587639

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A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Book Synopsis Nonlinear Oscillations and Waves in Dynamical Systems by : P.S Landa

Download or read book Nonlinear Oscillations and Waves in Dynamical Systems written by P.S Landa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.

Nonlinear Wave Dynamics of Materials and Structures

Author: Holm Altenbach

Publisher: Springer Nature

Published: 2020-04-22

Total Pages: 473

ISBN-13: 3030387089

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This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Book Synopsis Nonlinear Wave Dynamics of Materials and Structures by : Holm Altenbach

Download or read book Nonlinear Wave Dynamics of Materials and Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2020-04-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Nonlinear Wave Dynamics

Author: Patrick Lynett

Publisher: World Scientific

Published: 2009

Total Pages: 314

ISBN-13: 9812709045

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In September 2006, research leaders in the field of coastal engineering, fluid mechanics, and wave theory met at Cornell University to celebrate the 60th birthday of Prof. Philip L-F Liu. This volume is a compilation of the research papers presented at the symposium, and includes both review and new research papers. Topics such as nonlinear wave theory, tsunamis, wave-structure interaction, turbulence, and modeling of complex sediment transport are discussed in this volume. All of the contributing authors are research collaborators of Prof. Liu, and include leaders in coastal engineering such as Maarten Dingemans, Hwung-Hweng Hwung, Nobu Kobayashi, Inigo Losada, Hocine Oumeraci, Costas Synolakis, and Harry Yeh.

Book Synopsis Nonlinear Wave Dynamics by : Patrick Lynett

Download or read book Nonlinear Wave Dynamics written by Patrick Lynett and published by World Scientific. This book was released on 2009 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In September 2006, research leaders in the field of coastal engineering, fluid mechanics, and wave theory met at Cornell University to celebrate the 60th birthday of Prof. Philip L-F Liu. This volume is a compilation of the research papers presented at the symposium, and includes both review and new research papers. Topics such as nonlinear wave theory, tsunamis, wave-structure interaction, turbulence, and modeling of complex sediment transport are discussed in this volume. All of the contributing authors are research collaborators of Prof. Liu, and include leaders in coastal engineering such as Maarten Dingemans, Hwung-Hweng Hwung, Nobu Kobayashi, Inigo Losada, Hocine Oumeraci, Costas Synolakis, and Harry Yeh.

Tsunami and Nonlinear Waves

Author: Anjan Kundu

Publisher: Springer Science & Business Media

Published: 2007-06-19

Total Pages: 319

ISBN-13: 3540712569

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The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

Book Synopsis Tsunami and Nonlinear Waves by : Anjan Kundu

Download or read book Tsunami and Nonlinear Waves written by Anjan Kundu and published by Springer Science & Business Media. This book was released on 2007-06-19 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The need for tsunami research and analysis has grown dramatically following the devastating tsunami of December 2004, which affected Southern Asia. This book pursues a detailed theoretical and mathematical analysis of the fundamentals of tsunamis, especially the evolution and dynamics of tsunamis and other great waves. Of course, it includes specific measurement results from the 2004 tsunami, but the emphasis is on the nature of the waves themselves and their links to nonlinear phenomena.

Wave Dynamics of Generalized Continua

Author: Alexander G. Bagdoev

Publisher: Springer

Published: 2015-09-25

Total Pages: 274

ISBN-13: 3642372678

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This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with cavities, preliminary deformed disperse medium, solid with porosity filled by the electrically conductive and non-conductive liquid, magnetoelastic, piezo-semiconductors, crystals with dislocations, composites with inclusions, an electrically conductive asymmetrical liquid, a mixture of gas with a drop liquid. The book also considers the propagation of a laser beam through a two-level medium. The presented results are based on methods of evolution and modulation equations that were developed by the authors. The book is intended for scientific and technical researchers, students and post-graduate students specializing in mechanics of continuous media, physical acoustics, and physics of the solid state.

Book Synopsis Wave Dynamics of Generalized Continua by : Alexander G. Bagdoev

Download or read book Wave Dynamics of Generalized Continua written by Alexander G. Bagdoev and published by Springer. This book was released on 2015-09-25 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with cavities, preliminary deformed disperse medium, solid with porosity filled by the electrically conductive and non-conductive liquid, magnetoelastic, piezo-semiconductors, crystals with dislocations, composites with inclusions, an electrically conductive asymmetrical liquid, a mixture of gas with a drop liquid. The book also considers the propagation of a laser beam through a two-level medium. The presented results are based on methods of evolution and modulation equations that were developed by the authors. The book is intended for scientific and technical researchers, students and post-graduate students specializing in mechanics of continuous media, physical acoustics, and physics of the solid state.