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Author : Philip Barnes Burt
Publisher : CRC Press
Page : 352 pages
File Size : 46,8 Mb
Release : 1981
Category : Science
ISBN : 3718600722
Author : Angela Slavova,Petar Radoev Popivanov
Publisher : World Scientific Publishing
Page : 208 pages
File Size : 43,6 Mb
Release : 2018-11-16
Category : Mathematics
ISBN : 9789813271623
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 : Xiao-Feng Pang
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 44,7 Mb
Release : 2015
Category : Nonlinear theories
ISBN : 1611220114
This book describes complete nonlinear quantum mechanics, in which the fundamental and necessity theoretical principle and wave-corpuscle duality of microscopic particles were the foundation of this principle and its experimental evidences, the mechanisms of generation of the nonlinear interactions and its effects, as well as the methods solving nonlinear quantum mechanical problems, its distinctions with linear quantum mechanics and early nonlinear quantum mechanical idea and models, the completeness and correctness and universality of new theory as well as its applications in different systems containing polymers, physical and biological systems, which are exhibited in this book. Plenty of interesting results of these systems and a large number of novel properties of microscopic particles including the electron, proton, phonon, photon, exciton, polaron, magnon and Boson involving their localisations and classical features are stated in detail. This book is intended for researchers, teachers, graduate students, and upper level undergraduate students.
Author : J. R. Croca
Publisher : World Scientific
Page : 228 pages
File Size : 48,7 Mb
Release : 2003
Category : Science
ISBN : 9789812382108
Annotation Presents conceptual and experimental evidence showing that Heisenberg's uncertainty relations are not valid in all cases. The results lead to a coherent and beautiful causal synthesis unifying quantum and classical physics.
Author : Xiao-Feng Pang,Yuan-Ping Feng
Publisher : World Scientific
Page : 646 pages
File Size : 45,7 Mb
Release : 2005
Category : Science
ISBN : 9789812561169
In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.
Author : Dieter Schuch
Publisher : Springer
Page : 258 pages
File Size : 48,7 Mb
Release : 2018-01-20
Category : Science
ISBN : 9783319655949
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
Author : Fatkhulla Abdullaev,Vladimir V. Konotop
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 47,9 Mb
Release : 2006-03-02
Category : Science
ISBN : 9781402021909
Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Author : Andrei V. Gaponov-Grekhov,Mikhail I. Rabinovich,Jüri Engelbrecht
Publisher : Springer Science & Business Media
Page : 187 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642743665
Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet scientists working in this field. Instead of producing for the first time English proceedings it has been decided to present a good cross section of nonlinear physics in the USSR. Thus the participants at the last School were invited to provide English reviews and research papers for these two volumes (which in the years to come will be followed by the proceedings of forthcoming schools). The second volume deals with dynamical chaos in classical and quantum systems, with evolution in chemical systems and self-organisation in biology, and with applications of nonlinear dynamics to condensed matter, sea waves, and astrophysics.
Author : Jianke Yang
Publisher : SIAM
Page : 453 pages
File Size : 51,5 Mb
Release : 2010-01-01
Category : Science
ISBN : 9780898719680
Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.
Author : Eryk Infeld,George Rowlands
Publisher : Cambridge University Press
Page : 416 pages
File Size : 51,6 Mb
Release : 2000-07-13
Category : Mathematics
ISBN : 0521635578
The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Author : Stephen Nettel
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 46,9 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662053171
This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
Author : Stephen Nettel
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 46,6 Mb
Release : 2008-11-21
Category : Science
ISBN : 9783540879084
This textbook gives a detailed explanation of waves and oscillations in classical physics. These classical phenomena are dealt with at a more advanced level than is customary for second-year courses. All aspects of classical wave physics are presented, including the mathematical and physical basis needed for extended understanding. Finally several chapters are devoted to important topics in current wave physics. Special attention is given to nonlinear waves, solitons, chaotic behavior and associated phenomena. The new edition contains improvements such as full development of Greens functions, a broadening of the treatment of wave mechanics and a closer integration with classical mechanics, plus more examples and problems.
Author : Lokenath Debnath
Publisher : Cambridge University Press
Page : 372 pages
File Size : 45,6 Mb
Release : 2009-01-08
Category : Mathematics
ISBN : 9780511868610
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Author : A.D. Boardman,M. Bertolotti,T. Twardowski
Publisher : Springer Science & Business Media
Page : 498 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468458985
This book is based on the contributions to the 17th International School of Materials Sci ence and Technology, entitled Nonlinear Waves in Solid State Physics. This was held as a NATO Advanced Study Institute at the Ettore Majorana Centre in Erice, Sicily between the st th 1 and 15 July 1989, and attracted almost 100 participants from over 20 different countries. The book covers the fundamental properties of nonlinear waves in solid state materials, dealing with both theory and experiment. The aim is to emphasise the methods underpinning the important new developments in this area. The material is organised into subject areas that can broadly be classified into the following groups: the theory of nonlinear surface and guided waves in self-focusing magnetic and non-magnetic materials; nonlinear effects at in terfaces; nonlinear acoustoelectronic and surface acoustic waves; Lagrangian and Hamiltonian formulations of nonlinear problems; nonlinear effects in optical fibres; resonance phenomena; and nonlinear integrated optics. The chapters have been grouped together according to these classifications as closely as possible, but it should be borne in mind that although there is much overlap of ideas, each chapter is essentially independent of the others. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division, the European Physical Society, the National Science Foundation of the USA, the European Research Office, the Italian Ministry of Education, the Italian Ministry of Scientific and Technological Research, the Sicilian Regional Government and the Ugo Bordoni Foundation.
Author : Robert Hermann
Publisher : Unknown
Page : 610 pages
File Size : 40,8 Mb
Release : 1979
Category : Mathematics
ISBN : 0915692295
