On Multi Component Nonlinear Schrodinger Equation With Pt Symmetry
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| Author | : Demetrios Christodoulides |
| Publisher | : Springer |
| Total Pages | : 585 |
| Release | : 2018-11-28 |
| Genre | : Science |
| ISBN | : 9811312478 |
This book offers a comprehensive review of the state-of-the-art theoretical and experimental advances in linear and nonlinear parity-time-symmetric systems in various physical disciplines, and surveys the emerging applications of parity-time (PT) symmetry. PT symmetry originates from quantum mechanics, where if the Schrodinger operator satisfies the PT symmetry, then its spectrum can be all real. This concept was later introduced into optics, Bose-Einstein condensates, metamaterials, electric circuits, acoustics, mechanical systems and many other fields, where a judicious balancing of gain and loss constitutes a PT-symmetric system. Even though these systems are dissipative, they exhibit many signature properties of conservative systems, which make them mathematically and physically intriguing. Important PT-symmetry applications have also emerged. This book describes the latest advances of PT symmetry in a wide range of physical areas, with contributions from the leading experts. It is intended for researchers and graduate students to enter this research frontier, or use it as a reference book.
| Author | : Norbert Euler |
| Publisher | : CRC Press |
| Total Pages | : 367 |
| Release | : 2021-09-07 |
| Genre | : Mathematics |
| ISBN | : 1000423301 |
The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained
| Author | : Krassimir Georgiev |
| Publisher | : Springer |
| Total Pages | : 261 |
| Release | : 2017-02-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3319495445 |
This book presents recent research on Advanced Computing in Industrial Mathematics, which is one of the most prominent interdisciplinary areas and combines mathematics, computer science, scientific computations, engineering, physics, chemistry, medicine, etc. Further, the book presents the tools of Industrial Mathematics, which are based on mathematical models, and the corresponding computer codes, which are used to perform virtual experiments to obtain new data or to better understand the existing experimental results. The book gathers the peer-reviewed papers presented during the 10th Annual Meeting of the Bulgarian Section of SIAM (BGSIAM) from December 21 to 22, 2015 in Sofia, Bulgaria.
| Author | : Vladimir B. Matveev |
| Publisher | : Springer |
| Total Pages | : 122 |
| Release | : 1992-09-30 |
| Genre | : Science |
| ISBN | : 9783662009246 |
The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non linear evolution equations, including many important examples describing phe nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other "higher" levels of contemporary math ematics.
| Author | : M. J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 276 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 9780521534376 |
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
| Author | : S. Novikov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 1984-05-31 |
| Genre | : Mathematics |
| ISBN | : 9780306109775 |
| 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.
| Author | : Boris Malomed |
| Publisher | : MDPI |
| Total Pages | : 323 |
| Release | : 2018-03-23 |
| Genre | : Science |
| ISBN | : 3038426148 |
This book is a printed edition of the Special Issue "Guided-Wave Optics" that was published in Applied Sciences
| Author | : Vladimir Gerdjikov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 645 |
| Release | : 2008-06-02 |
| Genre | : Science |
| ISBN | : 3540770534 |
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
| Author | : Nick Laskin |
| Publisher | : World Scientific |
| Total Pages | : 358 |
| Release | : 2018-05-28 |
| Genre | : Science |
| ISBN | : 9813223812 |
Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics.This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework.Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process.The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.
