The Direct Method In Soliton Theory
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The Direct Method In Soliton Theory
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Author : Ryogo Hirota
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
The Direct Method In Soliton Theory written by Ryogo Hirota and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
Account of method of solving soliton equations by the inventor of the method.
The Direct Method In Soliton Theory
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Author :
language : en
Publisher:
Release Date : 2004
The Direct Method In Soliton Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Electronic books categories.
The modern version of the bilinear, or Hirota's direct, method is described here using relatively simple mathematics. As the only account in book form of the modern form of the theory, it will be essential reading for all those working in soliton theory.
Solitons
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Author : R.K. Bullough
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Solitons written by R.K. Bullough and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
With contributions by numerous experts
Loop Like Solitons In The Theory Of Nonlinear Evolution Equations
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Author : V. O. Vakhnenko
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-02-17
Loop Like Solitons In The Theory Of Nonlinear Evolution Equations written by V. O. Vakhnenko and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-17 with Science categories.
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.
Glimpses Of Soliton Theory
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Author : Alex Kasman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Glimpses Of Soliton Theory written by Alex Kasman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --
Nonlinear And Modern Mathematical Physics
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Author : Solomon Manukure
language : en
Publisher: Springer Nature
Release Date :
Nonlinear And Modern Mathematical Physics written by Solomon Manukure and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Research Advances In Chaos Theory
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Author : Paul Bracken
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-03-11
Research Advances In Chaos Theory written by Paul Bracken and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.
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.
Nonlinear Waves A Geometrical Approach
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Author : Angela Slavova
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-16
Nonlinear Waves A Geometrical Approach written by Angela Slavova and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-16 with Mathematics categories.
This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.
Nonlinear Optics
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Author : İlkay Bakırtaş
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-01-27
Nonlinear Optics written by İlkay Bakırtaş and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-27 with Science categories.
With this book, we aim to capture different perspectives of researchers on nonlinear optics and optical devices and we intend to cover the latest developments in optics from theoretical, numerical, and experimental aspects. The eleven selected chapters cover a variety of topics related to nonlinear optics including bright, dark, kink solitary waves in various media, magnetic solitons, lattice solitons, rogue-waves, solid-state lasers, laser cladding, optical sensors, optical vortices, and molecular switches. The book is intended to draw the attention of scientists in academia, as well as researchers and engineers in industry, since the field has a significant potential for the production and design of novel optical devices and other technological applications.
Solving Nonlinear Partial Differential Equations With Maple And Mathematica
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Author : Inna Shingareva
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-24
Solving Nonlinear Partial Differential Equations With Maple And Mathematica written by Inna Shingareva and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-24 with Mathematics categories.
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).