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Author: Ryogo Hirota
Publisher: Cambridge University Press
Published: 2004-07-22
Total Pages: 220
ISBN-13: 9780521836609
DOWNLOAD EBOOK →Account of method of solving soliton equations by the inventor of the method.
Author:
Publisher:
Published: 2004
Total Pages: 200
ISBN-13: 9780511214844
DOWNLOAD EBOOK →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.
Author: R.K. Bullough
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 403
ISBN-13: 3642814484
DOWNLOAD EBOOK →With contributions by numerous experts
Author: Robert M. Miura
Publisher: Springer
Published: 2006-11-14
Total Pages: 302
ISBN-13: 3540382208
DOWNLOAD EBOOK →Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Author: Angela Slavova
Publisher: Springer Nature
Published:
Total Pages: 483
ISBN-13: 3031532120
DOWNLOAD EBOOK →Author: Ivan V Cherednik
Publisher: World Scientific
Published: 1996-08-22
Total Pages: 264
ISBN-13: 9814499005
DOWNLOAD EBOOK →In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.
Author: Harendra Singh
Publisher: CRC Press
Published: 2022-02-17
Total Pages: 236
ISBN-13: 1000540103
DOWNLOAD EBOOK →Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
Author: Angela Slavova
Publisher: World Scientific Publishing
Published: 2018-11-16
Total Pages: 208
ISBN-13: 9813271620
DOWNLOAD EBOOK →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.
Author: Alwyn Scott
Publisher: Routledge
Published: 2006-05-17
Total Pages: 2881
ISBN-13: 1135455570
DOWNLOAD EBOOK →In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Author: Dr. K.S. Lakshmi
Publisher: Allied Publishers
Published: 2017-08-10
Total Pages: 196
ISBN-13: 9385926780
DOWNLOAD EBOOK →Differential Equations serve as mathematical models for virtually any natural or physical phenomena in science and technology and has applications even in diverse fields such as economics, medicine, ecology, etc. The seminar was organized to throw light on the recent advances in the applications of differential equations and to provide a platform for sharing the knowledge with experts in the field with young students and researchers. The Researchers and educators in the field of differential equations were invited to attend and share their rich experience. As for everything else. so for a mathematical theory. beauty can be perceived but not explained.
