Download or read book The sine Gordon Model and its Applications written by Jesús Cuevas-Maraver and published by Springer. This book was released on 2014-07-22 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.
Download or read book Topological and Non Topological Solitons in Scalar Field Theories written by Yakov M. Shnir and published by Cambridge University Press. This book was released on 2018-07-26 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to integrable and non-integrable scalar field models, with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, this book brings together discussion of solitary waves and construction of soliton solutions and provides a discussion of solitons using simple model examples.
Download or read book Soliton Theory and Its Applications written by Chaohao Gu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soliton theory is an important branch of applied mathematics and mathematical physics. An active and productive field of research, it has important applications in fluid mechanics, nonlinear optics, classical and quantum fields theories etc. This book presents a broad view of soliton theory. It gives an expository survey of the most basic ideas and methods, such as physical background, inverse scattering, Backlünd transformations, finite-dimensional completely integrable systems, symmetry, Kac-moody algebra, solitons and differential geometry, numerical analysis for nonlinear waves, and gravitational solitons. Besides the essential points of the theory, several applications are sketched and some recent developments, partly by the authors and their collaborators, are presented.
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2016-12-10 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.“div>This is a large interdisciplinary and interrelated field, and the present volume is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Download or read book The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics written by Georgios Pastras and published by Springer Nature. This book was released on 2020-10-31 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.
Download or read book Integrable Quantum Field Theories written by L. Bonora and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a NATO ARW held in Como, Italy, September 14-19, 1992
Download or read book Proceedings of the Second International A D Sakharov Conference on Physics written by Igor Michailovich Dremin and published by World Scientific. This book was released on 1997 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second International A D Sakharov Conference On Physics written by Igor Michailovich Dremin and published by World Scientific. This book was released on 1997-04-15 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the Second International A D Sakharov Conference on Physics, more than 200 physicists from many countries gathered together to celebrate what would have been the 75th birthday of the distinguished physicist and world figure Andrei Sakharov. This tradition had begun five years earlier, soon after his death.The conference was unique: it brought together leading scientists working in seemingly different fields, which were nevertheless among Sakharov's interests. Participants discussed the status and perspectives of research in high-energy physics, cosmology, astrophysics, classical and quantum gravity, plasma physics, nuclear physics, and extreme states of matter. The conference provided a unique opportunity for the participants to find and discuss common points of interest. The proceedings are evidence of the great variety of topics.Talks were given by distinguished physicists such as S Drell, L Okun, R Wilson, A D Linde, C W Misner, N A Popov, S L Adler, B DeWitt, M Kaku, J H Schwarz, A Zamolodchikov and E S Fradkin.
Download or read book Non equilibrium Dynamics of Tunnel Coupled Superfluids written by Marine Pigneur and published by Springer Nature. This book was released on 2020-08-28 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relaxation of isolated quantum many-body systems is a major unsolved problem of modern physics, which is connected to many fundamental questions. However, realizations of quantum many-body systems which are both well isolated from their environment and accessible to experimental study are scarce. In recent years, the field has experienced rapid progress, partly attributed to ultra-cold atoms. This book presents the experimental study of a relaxation phenomenon occurring in a one-dimensional bosonic Josephson junction. The system consists of two 1D quasi Bose-Einstein condensates of 87Rb, magnetically trapped on an atom chip. Using radio-frequency dressing, the author deforms a single harmonic trap, in which the atoms are initially condensed, into a double-well potential and realizes a splitting of the wave function. A large spatial separation and a tilt of the double-well enable the preparation of a broad variety of initial states by precisely adjusting the initial population and relative phase of the two wave packets, while preserving the phase coherence. By re-coupling the two wave packets, the author investigates tunneling regimes such as Josephson (plasma) oscillations and macroscopic quantum self-trapping. In both regimes, the tunneling dynamics exhibits a relaxation to a phase-locked equilibrium state contradicting theoretical predictions. The experimental results are supported with an empirical model that allows quantitative discussions according to various experimental parameters. These results illustrate how strongly the non-equilibrium dynamics differ from the equilibrium one, which is well described by thermodynamics and statistical physics.
Download or read book Conformal Field Theory and Solvable Lattice Models written by M Jimbo and published by Elsevier. This book was released on 2012-12-02 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.
Download or read book A Dynamical Perspective on the 4 Model written by Panayotis G. Kevrekidis and published by Springer. This book was released on 2019-02-26 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a careful selection of the most important developments of the \phi^4 model, offering a judicious summary of this model with a view to future prospects and the challenges ahead. Over the past four decades, the \phi^4 model has been the basis for a broad array of developments in the physics and mathematics of nonlinear waves. From kinks to breathers, from continuum media to discrete lattices, from collisions of solitary waves to spectral properties, and from deterministic to stochastic models of \phi^4 (and \phi^6, \phi^8, \phi^12 variants more recently), this dynamical model has served as an excellent test bed for formulating and testing the ideas of nonlinear science and solitary waves.
Download or read book Nonlinear Systems Vol 1 written by Victoriano Carmona and published by Springer. This book was released on 2018-09-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Download or read book Traveling Wave Analysis of Partial Differential Equations written by Graham Griffiths and published by Academic Press. This book was released on 2010-12-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors' intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net - Includes a spectrum of applications in science, engineering, applied mathematics - Presents a combination of numerical and analytical methods - Provides transportable computer codes in Matlab and Maple
Download or read book Some Musings on Theta Eta and Zeta written by Floyd L. Williams and published by Springer Nature. This book was released on with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Soliton Theory Applications to Mechanics written by Ligia Munteanu and published by Springer Science & Business Media. This book was released on 2006-07-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses.
Download or read book Wavelet Numerical Method and Its Applications in Nonlinear Problems written by You-He Zhou and published by Springer Nature. This book was released on 2021-03-09 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
Download or read book Problems of Nonlinear Mechanics and Physics of Materials written by Igor V. Andrianov and published by Springer. This book was released on 2018-07-31 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions on the current problems in a number of topical areas of nonlinear dynamics and physics, written by experts from Russia, Ukraine, Israel, Germany, Poland, Italy, the Netherlands, the USA, and France. The book is dedicated to Professor Leonid I. Manevitch, an outstanding scholar in the fields of Mechanics of Solids, Nonlinear Dynamics, and Polymer Physics, on the occasion of his 80th birthday.
