Scattering For First Order Linear Systems On The Line And B Cklund Transformations
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The Direct Method In Soliton Theory
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Author : Ryogo Hirota
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
The Direct Method In Soliton Theory written by Ryogo Hirota and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.
The Earth S Ionosphere
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Author : Michael C. Kelley
language : en
Publisher: Academic Press
Release Date : 1989
The Earth S Ionosphere written by Michael C. Kelley and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.
Suitable for advanced undergraduate and beginning graduate students in atmospheric, oceanic, and climate science, this textbook on the circulations of the atmosphere and ocean and their interaction emphasises on global scales. It gives students a grasp of what the atmosphere and oceans look like on the large-scale and why they look that way.
Nonlinear Waves
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Author : Lokenath Debnath
language : en
Publisher: CUP Archive
Release Date : 1983-12-30
Nonlinear Waves written by Lokenath Debnath and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-30 with Mathematics categories.
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Chemical Physics Of Intercalation
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Author : A.P. Legrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Chemical Physics Of Intercalation written by A.P. Legrand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Science categories.
Conjugated polymers suoh as polyaoetylene (CH)x polyphenylene (C6H4)x' poly thiophene (C4H2S)x' etc., which are insulators in their pristine state, can be brought to the metallic state after "doping" with ohemioal speoies whioh oan be either eleotron donors or I aoceptors. . This doping prooess involves a oharge transfer between the dopant moleoule and the polymer ohain whioh are then supposed to be spatially olose to each other. It follows that the meohanism of doping must be oonsidered as an aotual interoalation process, which will greatly affeot the struotural oharacteristios of the starting material, as well as its morphology, as has been observed during the 2 intercalation of graphite and layered compounds . In parallel with these modifioations, the band struoture of the system changes yielding a new set of eleotronio properties. It is evident therefore that the struotural and eleotronio properties are intimately related, and must be studied simultaneously in the same system to give reliable information. A great number of studies have been devoted to the structural and electronic properties of conjugated polymers after a chemical or 2 electrochemical doping process . Most of these concern the properties of the system for a given dopant concentration. With this approach a universal pioture of the polymer/dopant system is very diffioult to obtain, as a comparison between different experiments is very hazardous. On the other hand, only a small number of measurements have been performed during the continuous electroohemioal doping of various polymers.
Radiological Safety Aspects Of The Operation Of Electron Linear Accelerators
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Author : William P. Swanson
language : en
Publisher: Bernan Press(PA)
Release Date : 1979
Radiological Safety Aspects Of The Operation Of Electron Linear Accelerators written by William P. Swanson and has been published by Bernan Press(PA) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Business & Economics categories.
Electron linear accelerators are being used throughout the world in increasing numbers in a variety of important applications. Foremost among these is their role in the treatment of cancer. Commercial uses include non-destructive testing by radiography, food preservation, product sterilization and radiation processing of materials such as plastics and adhesives. Scientific applications include investigations in radiation biology, radiation chemistry, nuclear and elementary particle physics and radiation research. This manual provides authoritative guidance in radiation protection for this important category of radiation sources.
Spinach On The Ceiling The Multifaceted Life Of A Theoretical Chemist
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Author : Martin Karplus
language : en
Publisher: World Scientific
Release Date : 2020-06-22
Spinach On The Ceiling The Multifaceted Life Of A Theoretical Chemist written by Martin Karplus and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-22 with Science categories.
'Karplus's tales of a turbulent graduate school experience at Caltech will inspire readers to muster fortitude when everything seems to be spinning out of control. Karplus balances rigorous scientific discussions with refreshing chapters expounding his passion for photography and gastronomy.'Nature Chemistry, May 2020Nobel Laureate Martin Karplus was eight when his family fled Nazi-occupied Austria via Switzerland and France for the United States. He would later credit his life as a refugee as a decisive influence on his world view and approach to science.Spinach on the Ceiling is an autobiographical telling of Karplus' life story, and how it led him to win the Nobel Prize in Chemistry in 2013. The book captures pivotal moments in Martin's life — from his escape to Switzerland in 1938 shortly after Hitler's entrance into Austria; to memorable moments like when his parents gave him a microscope which opened his eyes to the wonders of science; to his education in New England and California; and his eventual scientific career which took him to England, Illinois, Columbia, Strasbourg, and Harvard. It relates how Martin's optimistic outlook and belief in his vision made it possible for him to overcome setbacks in his life, and turn a subject of study his colleagues considered a waste of time into a central part of chemistry and structural biology. It is his hope to inspire and aid young readers, in particular, to have a successful trajectory in their own lives. Although research and teaching have been his primary focus, he has traveled the world photographing people and places with a Leica IIIC and has had numerous exhibitions of the photographs. He has also enjoyed a lifelong interest in cooking and worked in some of the best restaurants in France and Spain.
Solitons Nonlinear Evolution Equations And Inverse Scattering
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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 1991-12-12
Solitons Nonlinear Evolution Equations And Inverse Scattering written by Mark J. Ablowitz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-12-12 with Mathematics categories.
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Scattering For First Order Linear Systems On The Line And B Cklund Transformations
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Author : Victor Daniel Zurkowski
language : en
Publisher:
Release Date : 1987
Scattering For First Order Linear Systems On The Line And B Cklund Transformations written by Victor Daniel Zurkowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Direct And Inverse Scattering On The Line
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Author : Richard Beals
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Direct And Inverse Scattering On The Line written by Richard Beals and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Deals with the theory of linear ordinary differential operators of arbitrary order. This book centers on the construction of special eigenfunctions and on the inverse problem. It is suitable for mathematicians, physicists, and engineers in the area of soliton equations, as well as those interested in the analytical aspects of inverse scattering.
Scattering And Inverse Scattering On The Line For A First Order System With Energy Dependent Potentials
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Author : Ramazan Ercan
language : en
Publisher:
Release Date : 2019
Scattering And Inverse Scattering On The Line For A First Order System With Energy Dependent Potentials written by Ramazan Ercan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Differential equations, Linear categories.
A first-order system of two linear ordinary differential equations is analyzed. The linear system contains a spectral parameter, and it has two coefficients that are functions of the spatial variable x. Those two functions act as potentials in the linear system and they also linearly contain the spectral parameter ʎ, and hence they are referred to as energy-dependent potentials. Such a linear system arises in the solution to a pair of integrable nonlinear partial differential equations (known as the derivative nonlinear Schr ̈odinger equations) via the so-called inverse scattering transform method.The direct and inverse problems for the corresponding first-order linear system with energy-dependent potentials are investigated. In the direct problem, when the two potentials belong to the Schwartz class, the properties of the corresponding scattering coefficients and so-called bound-state data are derived. In the inverse problem, the two potentials are recovered from the scattering data set consisting of the scattering coefficients and bound-state data. The solutions to the direct and inverse problems are achieved by relating the scattering data and the potentials in the energy-dependent system to those in a pair of first-order system with energy independent potentials. An alternate solution to the inverse problem is given by formulating a linear integral equation (referred to as the alternate Marchenko integral equation), and the energy-dependent potentials are recovered with the help of the solution to the alternate Marchenko equation.