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Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations PDF
Author: Pham Loi Vu
Publisher: CRC Press
ISBN: 100070906X
Size: 24.31 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 388
View: 4811

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Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations

by Pham Loi Vu, Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations Books available in PDF, EPUB, Mobi Format. Download Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations books, Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features • The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. • Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. • The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. • Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.




Neoclassical Analysis

Neoclassical Analysis PDF
Author: Mark Burgin
Publisher: Nova Science Pub Incorporated
ISBN:
Size: 25.18 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 396
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Neoclassical Analysis

by Mark Burgin, Neoclassical Analysis Books available in PDF, EPUB, Mobi Format. Download Neoclassical Analysis books, Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis. Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications. Consequently, new results are obtained extending and even completing classical theorems. In addition, facilities of analytical methods for various applications also become more broad and efficient.




Vietnam Journal

Vietnam Journal PDF
Author:
Publisher:
ISBN:
Size: 40.17 MB
Format: PDF, Docs
Category : Civil rights
Languages : en
Pages :
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Vietnam Journal

by , Vietnam Journal Books available in PDF, EPUB, Mobi Format. Download Vietnam Journal books,




Generalized Convexity Generalized Monotonicity And Applications

Generalized Convexity  Generalized Monotonicity and Applications PDF
Author: Andrew Eberhard
Publisher: Springer Science & Business Media
ISBN: 0387236392
Size: 36.30 MB
Format: PDF, Docs
Category : Business & Economics
Languages : en
Pages : 350
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Generalized Convexity Generalized Monotonicity And Applications

by Andrew Eberhard, Generalized Convexity Generalized Monotonicity And Applications Books available in PDF, EPUB, Mobi Format. Download Generalized Convexity Generalized Monotonicity And Applications books, In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.




Special Issue Proceedings Of International Winter School Geometry Education And Research

Special Issue  Proceedings of International Winter School  Geometry  Education and Research  PDF
Author: Martin A. Guest
Publisher:
ISBN:
Size: 72.74 MB
Format: PDF, Kindle
Category :
Languages : en
Pages : 121
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Special Issue Proceedings Of International Winter School Geometry Education And Research

by Martin A. Guest, Special Issue Proceedings Of International Winter School Geometry Education And Research Books available in PDF, EPUB, Mobi Format. Download Special Issue Proceedings Of International Winter School Geometry Education And Research books,