Self Focusing In The Perturbed And Unperturbed Nonlinear Schrodinger Equation In Critical Dimension
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| Author | : Gadi Fibich |
| Publisher | : Springer |
| Total Pages | : 870 |
| Release | : 2015-03-06 |
| Genre | : Mathematics |
| ISBN | : 3319127489 |
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrödinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. “This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics). It will be extremely useful for students and researchers who enter this field.” Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
| Author | : John M. Jarem |
| Publisher | : CRC Press |
| Total Pages | : 434 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 1439804230 |
This text examines a variety of spectral computational techniques— including k-space theory, Floquet theory and beam propagation— that are used to analyze electromagnetic and optical problems. The authors tie together different applications in EM and optics in which the state variable method is used. Emphasizing the analysis of planar diffraction gratings using rigorous coupled wave analysis, the book presents many cases that are analyzed using a full-field vector approach to solve Maxwell’s equations in anisotropic media where a standard wave equation approach is intractable.
| Author | : Nikolaos A. Kampanis |
| Publisher | : CRC Press |
| Total Pages | : 707 |
| Release | : 2008-02-25 |
| Genre | : Mathematics |
| ISBN | : 1420010875 |
Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable
| Author | : John M. Jarem |
| Publisher | : CRC Press |
| Total Pages | : 426 |
| Release | : 2016-04-19 |
| Genre | : Science |
| ISBN | : 1439891281 |
The current rapid and complex advancement applications of electromagnetic (EM) and optical systems calls for a much needed update on the computational methods currently in use. Completely revised and reflecting ten years of develoments, this second edition of the bestselling Computational Methods for Electromagnetic and Optical Systems provides the
| Author | : Catherine Sulem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2007-06-30 |
| Genre | : Mathematics |
| ISBN | : 0387227687 |
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
| Author | : Mark J. Ablowitz |
| Publisher | : Cambridge University Press |
| Total Pages | : 363 |
| Release | : 2011-09-08 |
| Genre | : Mathematics |
| ISBN | : 1139503480 |
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
| Author | : Emmanuel Kengne |
| Publisher | : Springer Nature |
| Total Pages | : 525 |
| Release | : 2023-02-23 |
| Genre | : Science |
| ISBN | : 981196744X |
This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
| Author | : Juan F. R. Archilla |
| Publisher | : Springer |
| Total Pages | : 572 |
| Release | : 2015-07-31 |
| Genre | : Technology & Engineering |
| ISBN | : 3319210459 |
This book presents the current knowledge about nonlinear localized travelling excitations in crystals. Excitations can be vibrational, electronic, magnetic or of many other types, in many different types of crystals, as silicates, semiconductors and metals. The book is dedicated to the British scientist FM Russell, recently turned 80. He found 50 years ago that a mineral mica muscovite was able to record elementary charged particles and much later that also some kind of localized excitations, he called them quodons, was also recorded. The tracks, therefore, provide a striking experimental evidence of quodons existence. The first chapter by him presents the state of knowledge in this topic. It is followed by about 18 chapters from world leaders in the field, reviewing different aspects, materials and methods including experiments, molecular dynamics and theory and also presenting the latest results. The last part includes a personal narration of FM Russell of the deciphering of the marks in mica. It provides a unique way to present the science in an accessible way and also illustrates the process of discovery in a scientist's mind.
| Author | : Sergey Yurish |
| Publisher | : Lulu.com |
| Total Pages | : 360 |
| Release | : 2018-04-27 |
| Genre | : Technology & Engineering |
| ISBN | : 846979437X |
'Advances in Optics: Reviews' Book Series is a comprehensive study of the field of optics, which provides readers with the most up-to-date coverage of optics, photonics and lasers with a good balance of practical and theoretical aspects. Directed towards both physicists and engineers this Book Series is also suitable for audiences focusing on applications of optics. The Vol.2 is devoted to lasers and photonics, and contains 15 chapters written by 40 authors from 15 countries: Algeria, Australia, Canada, China, Ecuador, Finland, France, Germany, India, Mexico, Poland, Qatar, Spain, Turkey and USA. A clear comprehensive presentation makes these books work well as both a teaching resources and a reference books. The book is intended for researchers and scientists in physics and optics, in academia and industry, as well as postgraduate students.
| Author | : |
| Publisher | : |
| Total Pages | : 762 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : |
