Loop-like Solitons in the Theory of Nonlinear Evolution Equations

Loop-like Solitons in the Theory of Nonlinear Evolution Equations
Title Loop-like Solitons in the Theory of Nonlinear Evolution Equations PDF eBook
Author V. O. Vakhnenko
Publisher Cambridge Scholars Publishing
Total Pages 240
Release 2022-02-17
Genre 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.

Nonlinear Evolution Equations and Dynamical Systems

Nonlinear Evolution Equations and Dynamical Systems
Title Nonlinear Evolution Equations and Dynamical Systems PDF eBook
Author Sandra Carillo
Publisher Springer Science & Business Media
Total Pages 247
Release 2012-12-06
Genre 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.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

Solitons, Nonlinear Evolution Equations and Inverse Scattering
Title Solitons, Nonlinear Evolution Equations and Inverse Scattering PDF eBook
Author Mark J. Ablowitz
Publisher
Total Pages 529
Release 1991
Genre 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.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

Solitons, Nonlinear Evolution Equations and Inverse Scattering
Title Solitons, Nonlinear Evolution Equations and Inverse Scattering PDF eBook
Author M. A. Ablowitz
Publisher
Total Pages 532
Release 1991
Genre 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.

Lectures on Nonlinear Evolution Equations

Lectures on Nonlinear Evolution Equations
Title Lectures on Nonlinear Evolution Equations PDF eBook
Author Reinhard Racke
Publisher Birkhäuser
Total Pages 315
Release 2015-08-31
Genre 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.

Nonlinear Evolution Equations and Related Topics

Nonlinear Evolution Equations and Related Topics
Title Nonlinear Evolution Equations and Related Topics PDF eBook
Author Wolfgang Arendt
Publisher Birkhäuser
Total Pages 803
Release 2012-12-06
Genre 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.

Research Advances in Chaos Theory

Research Advances in Chaos Theory
Title Research Advances in Chaos Theory PDF eBook
Author Paul Bracken
Publisher BoD – Books on Demand
Total Pages 138
Release 2020-03-11
Genre 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.