Long-time Dynamics of Korteweg-de Vries Solitary Waves Over a Variable Bottom

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ISBN 13 : 9780494219140
Total Pages : 158 pages
Book Rating : 4.2/5 (191 download)

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Book Synopsis Long-time Dynamics of Korteweg-de Vries Solitary Waves Over a Variable Bottom by : Steven Ivan Dejak

Download or read book Long-time Dynamics of Korteweg-de Vries Solitary Waves Over a Variable Bottom written by Steven Ivan Dejak and published by . This book was released on 2006 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the dynamics of solitons of KdV-type equations arising in the theory of shallow water waves propagating over channels with variable bottom. Under a rescaling, these waves satisfy the variable bottom generalized Korteweg-de Vries (bKdV) equation & part;tu = - & part;x(62x u + f(u) - b(t, x)u) with f = u2 and b related to the varying channel depth. The main result of the thesis is concerned with solitary wave dynamics of the bKdV with f a general nonlinearity (modulo some constraints) and b a small, bounded and slowly varying function. We prove that under suitable conditions on b and f, the bKdV is globally well-posed. With the knowledge that solutions exist, we study the long time behaviour of solutions with initial conditions close to a stable, b = 0 solitary wave. We prove that for long time intervals, such solutions have the form of a solitary wave, whose centre and scale evolve according to a certain dynamcal law involving the function b(t, x), plus an H 1(R)-small fluctuation. As motivation, we also describe how the bKdV equation appears in the field of water waves.

Slowly Varying Solitary Waves, 1; Korteweg-de Vries Equation

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ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Slowly Varying Solitary Waves, 1; Korteweg-de Vries Equation by : R. Grimshaw

Download or read book Slowly Varying Solitary Waves, 1; Korteweg-de Vries Equation written by R. Grimshaw and published by . This book was released on 1979 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics of Complexity and Dynamical Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 1461418054
Total Pages : 1885 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Complex Hamiltonian Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 364227305X
Total Pages : 277 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Complex Hamiltonian Dynamics by : Tassos Bountis

Download or read book Complex Hamiltonian Dynamics written by Tassos Bountis and published by Springer Science & Business Media. This book was released on 2012-04-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.

Nonlinear Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 3642556884
Total Pages : 628 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan

Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

Abstracts of Papers Presented to the American Mathematical Society

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ISBN 13 :
Total Pages : 826 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society

Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2004 with total page 826 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Waves

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Publisher : CUP Archive
ISBN 13 : 9780521254687
Total Pages : 376 pages
Book Rating : 4.2/5 (546 download)

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Book Synopsis Nonlinear Waves by : Lokenath Debnath

Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On Cylindrical Solitary Waves

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ISBN 13 :
Total Pages : 94 pages
Book Rating : 4.3/5 (121 download)

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Book Synopsis On Cylindrical Solitary Waves by : Henry Power Meneses

Download or read book On Cylindrical Solitary Waves written by Henry Power Meneses and published by . This book was released on 1982 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Dynamical Systems

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Publisher : Gulf Professional Publishing
ISBN 13 : 0080532845
Total Pages : 1099 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Dynamical Systems by : B. Fiedler

Download or read book Handbook of Dynamical Systems written by B. Fiedler and published by Gulf Professional Publishing. This book was released on 2002-02-21 with total page 1099 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Dispersive Long Waves of Finite Amplitiude Over an Uneven Bottom

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ISBN 13 :
Total Pages : 101 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Dispersive Long Waves of Finite Amplitiude Over an Uneven Bottom by : Ole Secher Madsen

Download or read book Dispersive Long Waves of Finite Amplitiude Over an Uneven Bottom written by Ole Secher Madsen and published by . This book was released on 1969 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Partial Differential Equations and Solitary Waves Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 364200251X
Total Pages : 700 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Partial Differential Equations and Solitary Waves Theory by : Abdul-Majid Wazwaz

Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Report on Waves

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ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.A/5 ( download)

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Book Synopsis Report on Waves by : John Scott Russell

Download or read book Report on Waves written by John Scott Russell and published by . This book was released on 1845 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Waves and Nonlinear Processes in Hydrodynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 9400902530
Total Pages : 423 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Waves and Nonlinear Processes in Hydrodynamics by : John Grue

Download or read book Waves and Nonlinear Processes in Hydrodynamics written by John Grue and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In December 1994 Professor Enok Palm celebrated his 70th birthday and retired after more than forty years of service at the University of Oslo. In view of his outstanding achievements as teacher and scientist a symposium entitled "Waves and Nonlinear Processes in Hydrodynamics" was held in his honour from the 17th to the 19th November 1994 in the locations of The Norwegian Academy of Science and Letters in Oslo. The topics of the symposium were chosen to cover Enok's broad range of scientific work, interests and accomplishments: Marine hydrodynamics, nonlinear wave theory, nonlinear stability, thermal convection and geophys ical fluid dynamics, starting with Enok's present activity, ending with the field where he began his career. This order was followed in the symposium program. The symposium had two opening lectures. The first looked back on the history of hydrodynamic research at the University of Oslo. The second focused on applications of hydrodynamics in the offshore industry today.

Mathematical Reviews

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ISBN 13 :
Total Pages : 776 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation

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Publisher : SIAM
ISBN 13 : 9780898714708
Total Pages : 1062 pages
Book Rating : 4.7/5 (147 download)

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Book Synopsis Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation by : Alfredo Berm?dez

Download or read book Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation written by Alfredo Berm?dez and published by SIAM. This book was released on 2000-01-01 with total page 1062 pages. Available in PDF, EPUB and Kindle. Book excerpt: This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.

Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid

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ISBN 13 : 9780868390796
Total Pages : 46 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid by : Roger Grimshaw

Download or read book Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid written by Roger Grimshaw and published by . This book was released on 1984 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solitons

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Publisher : Cambridge University Press
ISBN 13 : 9780521336550
Total Pages : 244 pages
Book Rating : 4.3/5 (365 download)

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Book Synopsis Solitons by : P. G. Drazin

Download or read book Solitons written by P. G. Drazin and published by Cambridge University Press. This book was released on 1989-02-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is an introduction to the theory of solitons in the physical sciences.