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Author: Panayotis G. Kevrekidis Publisher: Springer Science & Business Media ISBN: 3540891994 Category : Science Languages : en Pages : 417
Book Description
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.
Author: Panayotis G. Kevrekidis Publisher: Springer Science & Business Media ISBN: 3540891994 Category : Science Languages : en Pages : 417
Book Description
This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes.
Author: M. J. Ablowitz Publisher: Cambridge University Press ISBN: 9780521534376 Category : Mathematics Languages : en Pages : 276
Book Description
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.
Author: Luis Vazquez Publisher: World Scientific ISBN: 9814486515 Category : Technology & Engineering Languages : en Pages : 363
Book Description
This conference was the third meeting organized in the framework of the European LOCNET project. The main topics discussed by this international research collaboration were localization by nonlinearity and spatial discreteness, and energy transfer (in crystals, biomolecules and Josephson arrays).
Author: Catherine Sulem Publisher: Springer Science & Business Media ISBN: 0387227687 Category : Mathematics Languages : en Pages : 363
Book Description
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: SIAM ISBN: 089871477X Category : Mathematics Languages : en Pages : 433
Book Description
A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Author: Galina Filipuk Publisher: Springer ISBN: 3319991485 Category : Mathematics Languages : en Pages : 273
Book Description
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
Author: Joachim Weidmann Publisher: Springer Science & Business Media ISBN: 1461260272 Category : Mathematics Languages : en Pages : 413
Book Description
This English edition is almost identical to the German original Lineare Operatoren in Hilbertriiumen, published by B. G. Teubner, Stuttgart in 1976. A few proofs have been simplified, some additional exercises have been included, and a small number of new results has been added (e.g., Theorem 11.11 and Theorem 11.23). In addition a great number of minor errors has been corrected. Frankfurt, January 1980 J. Weidmann vii Preface to the German edition The purpose of this book is to give an introduction to the theory of linear operators on Hilbert spaces and then to proceed to the interesting applica tions of differential operators to mathematical physics. Besides the usual introductory courses common to both mathematicians and physicists, only a fundamental knowledge of complex analysis and of ordinary differential equations is assumed. The most important results of Lebesgue integration theory, to the extent that they are used in this book, are compiled with complete proofs in Appendix A. I hope therefore that students from the fourth semester on will be able to read this book without major difficulty. However, it might also be of some interest and use to the teaching and research mathematician or physicist, since among other things it makes easily accessible several new results of the spectral theory of differential operators.
Author: Sergey Nazarenko Publisher: Springer Science & Business Media ISBN: 3642159419 Category : Science Languages : en Pages : 287
Book Description
Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
Author: Panayotis G. Kevrekidis
Author: Panayotis G. Kevrekidis
Author: M. J. Ablowitz
Author: USAMA. AL KHAWAJA
Author: Luis Vazquez
Author: Catherine Sulem
Author: Mark J. Ablowitz
Author: Galina Filipuk
Author: Joachim Weidmann
Author: Sergey Nazarenko
Author: P. G. Drazin