The Direct Method in Soliton Theory
Title | The Direct Method in Soliton Theory PDF eBook |
Author | Ryogo Hirota |
Publisher | Cambridge University Press |
Total Pages | 220 |
Release | 2004-07-22 |
Genre | Mathematics |
ISBN | 9780521836609 |
Account of method of solving soliton equations by the inventor of the method.
The Direct Method in Soliton Theory
Title | The Direct Method in Soliton Theory PDF eBook |
Author | |
Publisher | |
Total Pages | 200 |
Release | 2004 |
Genre | Electronic books |
ISBN | 9780511214844 |
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
Title | Solitons PDF eBook |
Author | R.K. Bullough |
Publisher | Springer Science & Business Media |
Total Pages | 403 |
Release | 2013-11-11 |
Genre | Science |
ISBN | 3642814484 |
With contributions by numerous experts
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 |
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
Title | Glimpses of Soliton Theory PDF eBook |
Author | Alex Kasman |
Publisher | American Mathematical Soc. |
Total Pages | 322 |
Release | 2010 |
Genre | Mathematics |
ISBN | 0821852450 |
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 Waves: A Geometrical Approach
Title | Nonlinear Waves: A Geometrical Approach PDF eBook |
Author | Angela Slavova |
Publisher | World Scientific Publishing |
Total Pages | 208 |
Release | 2018-11-16 |
Genre | Mathematics |
ISBN | 9813271620 |
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 and Modern Mathematical Physics
Title | Nonlinear and Modern Mathematical Physics PDF eBook |
Author | Solomon Manukure |
Publisher | Springer Nature |
Total Pages | 389 |
Release | |
Genre | |
ISBN | 3031595394 |