Classical And Quantum Aspects Of Completely Integrable Nonlinear Systems
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Author | : A Kundu |
Publisher | : CRC Press |
Total Pages | : 310 |
Release | : 2019-04-23 |
Genre | : Science |
ISBN | : 1420034618 |
Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
Author | : |
Publisher | : |
Total Pages | : 184 |
Release | : 1980 |
Genre | : |
ISBN | : |
Author | : Asesh Roy Chowdhury |
Publisher | : CRC Press |
Total Pages | : 425 |
Release | : 2004-01-28 |
Genre | : Science |
ISBN | : 0203498011 |
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Author | : Krzysztof Kowalski |
Publisher | : World Scientific |
Total Pages | : 148 |
Release | : 1994-07-26 |
Genre | : Science |
ISBN | : 9814502057 |
This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrödinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the “quantal” Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bäcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.
Author | : Muthuswamy Lakshmanan |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642760465 |
Proceedings of the Workshop, Bharathidasan University, Tiruchirapalli, India, November 29 - December 2, 1989
Author | : Fatkhulla Abdullaev |
Publisher | : Springer Science & Business Media |
Total Pages | : 563 |
Release | : 2006-03-02 |
Genre | : Science |
ISBN | : 1402021909 |
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 | : Mauro Carfora |
Publisher | : World Scientific |
Total Pages | : 194 |
Release | : 1992-04-30 |
Genre | : |
ISBN | : 9814554766 |
This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.
Author | : A.K. Prykarpatsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 555 |
Release | : 2013-04-09 |
Genre | : Science |
ISBN | : 9401149941 |
In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Author | : Piergiulio Tempesta |
Publisher | : American Mathematical Soc. |
Total Pages | : 362 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821833294 |
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).
Author | : John P. Harnad |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821820931 |
This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.