[PDF] Loop Like Solitons In The Theory Of Nonlinear Evolution Equations eBook

Author : V. O. Vakhnenko
Publisher : Cambridge Scholars Publishing
Page : 240 pages
File Size : 28,85 MB
Release : 2022-02-17
Category : Science
ISBN : 1527581470

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This book shows that the physical phenomena and processes that take place in nature generally have complicated nonlinear features, which leads to nonlinear mathematical models for the real processes. It focuses on the practical issues involved here, as well as the development of methods to investigate the associated nonlinear mathematical problems, including nonlinear wave propagation. It acquaints the reader with a series of methods and approaches that can be applied to a wide class of nonlinear equations. The book also outlines a way in which an uninitiated reader could investigate a new nonlinear equation.

Author : Sandra Carillo
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 49,83 MB
Release : 2012-12-06
Category : Science
ISBN : 3642840396

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Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.

Author : Mark J. Ablowitz
Publisher :
Page : 529 pages
File Size : 34,1 MB
Release : 1991
Category : MATHEMATICS
ISBN : 9781107361614

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This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Author : M. A. Ablowitz
Publisher :
Page : 532 pages
File Size : 14,48 MB
Release : 1991
Category : Electronic books
ISBN : 9781107366527

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This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Author : Reinhard Racke
Publisher : Birkhäuser
Page : 315 pages
File Size : 32,63 MB
Release : 2015-08-31
Category : Mathematics
ISBN : 3319218735

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This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behaviour of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial boundary value problems and for open questions are provided. In this second edition, initial-boundary value problems in waveguides are additionally considered.

Author : Paul Bracken
Publisher : BoD – Books on Demand
Page : 138 pages
File Size : 21,6 MB
Release : 2020-03-11
Category : Mathematics
ISBN : 1789855438

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The subject of chaos has invaded practically every area of the natural sciences. Weather patterns are referred to as chaotic. There are chemical reactions and chaotic evolution of insect populations. Atomic and molecular physics have also seen the emergence of the study of chaos in these microscopic domains. This book examines the issue of chaos in nonlinear and dynamical systems, quantum mechanics, biology, and economics.

Author : Wolfgang Arendt
Publisher : Birkhäuser
Page : 803 pages
File Size : 20,68 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034879245

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Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.

Author : Songmu Zheng
Publisher : CRC Press
Page : 304 pages
File Size : 20,10 MB
Release : 2004-07-08
Category : Mathematics
ISBN : 0203492226

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Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques. These include the semigroup method, the compactness and monotone operator

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
Page : 166 pages
File Size : 41,84 MB
Release : 2022-12-06
Category : Mathematics
ISBN : 1527591557

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This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.