Discrete Nonlinear Schrodinger Equation Beyond Complete Integrability

Author : Guoping Zhang
Publisher :
ISBN 13 : 9789811290275
Total Pages : 0 pages
Book Rating : 4.7X/5 ( download)

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Download or read book Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability written by Guoping Zhang and published by . This book was released on 2024-07-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations appear as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be possible thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there are necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Author : M. J. Ablowitz
Publisher : Cambridge University Press
ISBN 13 : 9780521534376
Total Pages : 276 pages
Book Rating : 4.72/5 ( download)

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Download or read book Discrete and Continuous Nonlinear Schrödinger Systems written by M. J. Ablowitz and published by Cambridge University Press. This book was released on 2004 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Author : Panayotis G. Kevrekidis
Publisher : Springer Science & Business Media
ISBN 13 : 3540891994
Total Pages : 417 pages
Book Rating : 4.94/5 ( download)

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Download or read book The Discrete Nonlinear Schrödinger Equation written by Panayotis G. Kevrekidis and published by Springer Science & Business Media. This book was released on 2009-07-07 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Boiti
Publisher : World Scientific
ISBN 13 : 9814493937
Total Pages : 568 pages
Book Rating : 4.32/5 ( download)

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Download or read book Nonlinearity, Integrability And All That: Twenty Years After Needs '79 - Proceedings Of The Workshop written by M Boiti and published by World Scientific. This book was released on 2000-05-12 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems — classical and quantum — are considered.

Author : J. Hietarinta
Publisher : Cambridge University Press
ISBN 13 : 1107042720
Total Pages : 461 pages
Book Rating : 4.28/5 ( download)

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Download or read book Discrete Systems and Integrability written by J. Hietarinta and published by Cambridge University Press. This book was released on 2016-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Author : Lars Brink
Publisher : World Scientific
ISBN 13 : 9811263701
Total Pages : 341 pages
Book Rating : 4.05/5 ( download)

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Download or read book Looking Beyond The Frontiers Of Science: Dedicated To The 80th Birthday Of Kk Phua written by Lars Brink and published by World Scientific. This book was released on 2022-07-25 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Kok Khoo Phua is the Founding Director and Emeritus Professor of the Institute of Advanced Studies (IAS) at Nanyang Technological University (NTU) and Adjunct Professor of Department of Physics both at Nanyang Technological University (NTU) and National University of Singapore (NUS). He is the Chairman and Editor-in-Chief of World Scientific Publishing Co Pte Ltd.When he was elected a Fellow of the American Physical Society (APS) in 2009, the citation read: 'For tireless efforts to strengthen scientific research throughout Asia and promote international physics education and scholarly exchanges, and for enriching science and education through the World Scientific Publishing Company he founded.'This unique volume on the occasion of his 80th birthday is a compilation of tributes from his friends who have known him for decades along with scientific articles that celebrate his visionary approach to promote science worldwide.

Author : Spyridon Kamvissis
Publisher : Princeton University Press
ISBN 13 : 069111482X
Total Pages : 281 pages
Book Rating : 4.28/5 ( download)

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Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-09-07 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.

Author : Basil Grammaticos
Publisher : Springer
ISBN 13 : 9783540214250
Total Pages : 472 pages
Book Rating : 4.59/5 ( download)

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Download or read book Discrete Integrable Systems written by Basil Grammaticos and published by Springer. This book was released on 2004-06-22 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of a set of ten lectures conceived as both introduction and up-to-date survey on discrete integrable systems. It constitutes a companion book to "Integrability of Nonlinear Systems" (Springer-Verlag, 2004, LNP 638, ISBN 3-540-20630-2). Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.

Author : Alexander Mikhailov
Publisher : Springer Science & Business Media
ISBN 13 : 3540881107
Total Pages : 348 pages
Book Rating : 4.00/5 ( download)

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Download or read book Integrability written by Alexander Mikhailov and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable one and whether it can be studied in depth analytically. In this book we have tried to c- ate a mathematical framework to address these issues, and we give descriptions of methods and review results. In the Introduction we give a historical account of the birth and development of the theory of integrable equations, focusing on the main issue of the book – the concept of integrability itself. A universal de nition of Integrability is proving to be elusive despite more than 40 years of its development. Often such notions as “- act solvability” or “regular behaviour” of solutions are associated with integrable systems. Unfortunately these notions do not lead to any rigorous mathematical d- inition. A constructive approach could be based upon the study of hidden and rich algebraic or analytic structures associated with integrable equations. The requi- ment of existence of elements of these structures could, in principle, be taken as a de nition for integrability. It is astonishing that the nal result is not sensitive to the choice of the structure taken; eventually we arrive at the same pattern of eq- tions.

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206309
Total Pages : 358 pages
Book Rating : 4.02/5 ( download)

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Download or read book Integrability of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2004-02-17 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.