An overview of the basic concepts, methods and applications of nonlinear low-dimensional solid state physics based on the Frenkel--Kontorova model and its generalizations. The book covers many important topics such as the nonlinear dynamics of discrete systems, the dynamics of solitons and their interaction, commensurate and incommensurate systems, statistical mechanics of nonlinear systems, and nonequilibrium dynamics of interacting many-body systems.
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction arrays, waveguide arrays, photonic crystals and optical fibers. Nonlinear excitations are inherent to Bose-Einstein Condensates, constituting an excellent benchmark for testing their properties and providing a pathway for future discoveries in fundamental physics.
The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems — both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).
Pt. I. Analytical methods. On the IST for discrete nonlinear Schrödinger systems and polarization shift for discrete vector solitons / M.J. Ablowitz, B. Prinari, A.D. Trubatch -- Soliton solutions of coupled nonlinear Klein-Gordon equations / T. Alagesan -- Characteristic initial value problems for integrable hyperbolic reductions of Einstein's equations / G.A. Alekseev -- Discrete sine-Gordon equation / M. Boiti [und weitere] -- Integrable and non-integrable equations with peakons / A. Degasperis, D.D. Holm, A.N.W. Hone -- Solution of a free boundary problem for a nonlinear diffusion-convection equation / S. De Lillo, M.C. Salvatori, G. Sanchini -- Iterative construction of solutions for a nonisospectral problem in 2 + 1 dimensions / P.G. Estevez -- Discrete breathers close to the anticontinuum limit: existence and wave scattering / S. Flach [und weitere] -- Complex Toda chain - an integrable universal model for adiabatic N-soliton interactions! / V.S. Gerdjikov -- On the reductions and scattering data for the generalized Zakharov-Shabat systems / G.G. Grahovski -- Bilinear representation for the modified nonlinear Schrödinger equations and their quantum potential deformations / J.H. Lee, O.K. Pashaev -- Noncommutative Burgers' equations / L. Martina, O.K. Pashaev -- On the quasi-classical [sumbol]-dressing method / B. Konopelchenko, A. Moro -- New solvable matrix integrals - U(n) case / A. Yu. Orlov -- Integrable hydrodynamic chains / M.V. Pavlov -- KPII: new results and open problems / A.K. Pogrebkov -- A workmate for KdV / P.C. Sabatier -- Space-time lattice for operator Schrödinger equation / A. Spire, V.V. Konotop, L. Vazquez -- On isomonodromy deformations for the ZS-AKNS flows / D. Wu -- pt. II. Symmetry properties, Hamiltonian methods and group theoretical methods. New symmetry reductions for a lubrication model / M.S. Bruzón [und weitere] -- Quantum solitons for quantum information and quantum computing / R.K. Bullough, M. Wadati -- Solving renormalization group equations by recursion relations / A. Cafarella, C. Corianò, M. Guzzi -- A tri-Hamiltonian route to spectral curves / L. Degiovanni, G. Magnano -- Construction of real forms of complexified Hamiltonian dynamical systems / V.S. Gerdjikov [und weitere] -- Integrable and super-integrable systems in classical and quantum mechanics / M. Giordano [und weitere] -- Non-commuting coordinates in vortex dynamics and in the Hall effect, related to "exotic" Galilean symmetry / P.A. Horváthy -- Structure of multi-meron knot action / L.S. Isaev, A.P. Protogenov -- Compatible nonlocal Poisson brackets of hydrodynamic type and integrable reductions of the Lamé equations / O.I. Mokhov -- Pseudoanti-Hermiticity in QQM, time-reversal and Kramers degeneracy / G. Scolarici -- On the integrability of supersymmetric equations / P. Tempesta, R.A. Leo, G. Soliani
The investigation of the properties of nonlinear systems is one of the fast deve loping areas of physics. In condensed matter physics this 'terra incognita' is approached from various starting points such as phase transitions and renormali zation group theory, nonlinear models, statistical mechanics and others. The study of the mutual interrelations of these disciplines is important in developing uni fying methods and models towards a better understanding of nonlinear systems. The present book collects the lectures and seminars delivered at the workshop on "Statics and Dynamics of Nonlinear Systems" held at the Centre for SCientific Culture "Ettore Majorana·" in Erice;· Italy, July 1 to 11, 1983, in the framework of the International School of Materials Science and Technology. Experts and young researchers came together to discuss nonlinear phenomena in condensed matter physics. The book is divided into five parts, each part containing a few general artic les introducing the subject, followed by related specialized papers. The first part deals with basic properties of nonlinear systems including an introduction to the general theoretical methods. Contrfbutions to the nonlinear aspects of phase transitions are collected in the second part. In the third part properties of incommensurate systems are discussed. Here, competing interactions lead to charge-density waves, soliton lattices and other complex structures. Another point of special interest, illustrated in the fourth part, is the 'chaotic' be havior of various systems such as Josephson junctions and discrete lattices.
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.
Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schr?dinger-type models that arise therein.?The Defocusing Nonlinear Schr?dinger Equation?is a broad study of nonlinear?excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.
This is a unique book that presents rigorous mathematical results on Fermi-Pasta-Ulam lattices, a field of great interest in nonlinear analysis, nonlinear science, mathematical physics, etc. It considers travelling waves and time periodic oscillations in infinite Fermi-Pasta-Ulam lattices, which are not necessarily spatially homogenous. Similar systems, infinite chains of linearly coupled nonlinear oscillators, are also discussed. The book is self-contained and includes a number of open problems, making it suitable for use in a course for graduate students.
This handbook provides insights into becoming a better and more evolved athlete. It offers aspiring athletes, regardless of skill level, a better understanding of their bodies and how to unlock the unlimited potential of muscles without injury. It focuses on the “superhero” muscle: the iliopsoas, and also sheds light on Diamond-Corporation’s new technology and elite athleticism, and how these can contribute to a healthier life. Lastly, the authors explore the mindset of success and provide exercises for remaining calm under pressure. This stand-alone book is the sequel to Paradigm Shift for Future Tennis and Enhancing Performance and Reducing Stress in Sport (2014, Springer). This book is written by scientists, whose expertise collectively spans the fields of biomechanics, clinical surgery, current and former elite athleticism, engineering and naturopath doctoral work. Together, they aim to inspire and educate athletes on how to improve their sports performance by using new technologies, world class biomechanics knowledge and ancient herbal medicines.
