| Author | : S. Novikov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 1984-05-31 |
| Genre | : Mathematics |
| ISBN | : 9780306109775 |
Solitons and the Inverse Scattering Transform
| Author | : Mark J. Ablowitz |
| Publisher | : SIAM |
| Total Pages | : 433 |
| Release | : 2006-05-15 |
| Genre | : Mathematics |
| ISBN | : 089871477X |
A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications
| Author | : Robert M. Miura |
| Publisher | : Springer |
| Total Pages | : 302 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540382208 |
Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Solitons, Nonlinear Evolution Equations and Inverse Scattering
| Author | : Mark J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 532 |
| Release | : 1991-12-12 |
| Genre | : Mathematics |
| ISBN | : 0521387302 |
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
| Author | : Boling Guo |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 463 |
| Release | : 2018-03-19 |
| Genre | : Mathematics |
| ISBN | : 3110549417 |
This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics. Contents Introduction Inverse scattering transform Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations Interaction of solitons and its asymptotic properties Hirota method Bäcklund transformations and the infinitely many conservation laws Multi-dimensional solitons and their stability Numerical computation methods for some nonlinear evolution equations The geometric theory of solitons Global existence and blow up for the nonlinear evolution equations The soliton movements of elementary particles in nonlinear quantum field The theory of soliton movement of superconductive features The soliton movements in condensed state systemsontents
Introduction to non-Kerr Law Optical Solitons
| Author | : Anjan Biswas |
| Publisher | : CRC Press |
| Total Pages | : 211 |
| Release | : 2006-11-10 |
| Genre | : Mathematics |
| ISBN | : 1420011405 |
Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities. After an introduction to the basic features of fiber-optic com
Direct and Inverse Sturm-Liouville Problems
| Author | : Vladislav V. Kravchenko |
| Publisher | : Birkhäuser |
| Total Pages | : 154 |
| Release | : 2020-08-18 |
| Genre | : Mathematics |
| ISBN | : 9783030478483 |
This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.
