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(m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 065/5 ( reviews)

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Book Synopsis (m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions by : Fritz Gesztesy

Download or read book (m)KdV Solitons on the Background of Quasi-Periodic Finite-Gap Solutions written by Fritz Gesztesy. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: In the introductory section, we review the formulation of the Korteweg-de Vries (KdV) equation and of the modified KdV (mKdV) equation as a compatibility condition for a Lax pair of linear operators. We then illustrate Miura's transformation, which maps solutions of the mKdV into solutions of the KdV. We then give a general overview of the concept of soliton solutions relative to general backgrounds, and of the single and double commutation methods. Finally, we present the main results of the article. To avoid the clutter of too many technical details, the paper is organized in four sections and five appendices.

Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies

1998 Mathematics
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Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 087/5 ( reviews)

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Book Synopsis Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies by : Wolfgang Bulla

Download or read book Algebro-Geometric Quasi-Periodic Finite-Gap Solutions of the Toda and Kac-van Moerbeke Hierarchies written by Wolfgang Bulla. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the authors provide a self-contained discussion of all real-valued quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchies of completely integrable evolution equations. The approach utilizes algebro-geometric methods, factorization techniques for finite difference expressions, as well as Miura-type transformations. Detailed spectral theoretic properties of Lax pairs and theta function representations of the solutions are derived. Features: Simple and unified treatment of the topic. Self-contained development. Novel results for the Kac-van Moerbeke hierarchy and its algebro-geometric solutions.

Theory of Solitons

1984-05-31 Mathematics
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Release : 1984-05-31
Genre : Mathematics
Kind : eBook
Book Rating : 775/5 ( reviews)

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Book Synopsis Theory of Solitons by : S. Novikov

Download or read book Theory of Solitons written by S. Novikov. This book was released on 1984-05-31. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena

2010-10-01 Mathematics
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Release : 2010-10-01
Genre : Mathematics
Kind : eBook
Book Rating : 76X/5 ( reviews)

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Book Synopsis Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena by : Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations

Download or read book Nonlinear Partial Differential Equations and Hyperbolic Wave Phenomena written by Norske videnskaps-akademi. Research Program on Nonlinear Partial Differential Equations. This book was released on 2010-10-01. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the state of the art in several directions of research conducted by renowned mathematicians who participated in the research program on Nonlinear Partial Differential Equations at the Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway, during the academic year 2008-09. The main theme of the volume is nonlinear partial differential equations that model a wide variety of wave phenomena. Topics discussed include systems of conservation laws, compressible Navier-Stokes equations, Navier-Stokes-Korteweg type systems in models for phase transitions, nonlinear evolution equations, degenerate/mixed type equations in fluid mechanics and differential geometry, nonlinear dispersive wave equations (Korteweg-de Vries, Camassa-Holm type, etc.), and Poisson interface problems and level set formulations.

Operator Theory in Harmonic and Non-commutative Analysis

2014-06-21 Mathematics
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Release : 2014-06-21
Genre : Mathematics
Kind : eBook
Book Rating : 662/5 ( reviews)

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Book Synopsis Operator Theory in Harmonic and Non-commutative Analysis by : Joseph A. Ball

Download or read book Operator Theory in Harmonic and Non-commutative Analysis written by Joseph A. Ball. This book was released on 2014-06-21. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 23rd International Workshop on Operator Theory and its Applications (IWOTA 2012), which was held at the University of New South Wales (Sydney, Australia) from 16 July to 20 July 2012. It includes twelve articles presenting both surveys of current research in operator theory and original results.

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