Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)
Author: Spyridon Kamvissis
Publisher: Princeton University Press
Total Pages: 281
Release: 2003-09-07
Genre: Mathematics
ISBN: 069111482X

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.

Nonlinear Wave Equations

Nonlinear Wave Equations
Author: Christopher W. Curtis
Publisher: American Mathematical Soc.
Total Pages: 226
Release: 2015-03-26
Genre: Nonlinear wave equations
ISBN: 1470410508

This volume contains the proceedings of the AMS Special Session on Nonlinear Waves and Integrable Systems, held on April 13-14, 2013, at the University of Colorado, Boulder, Colorado. The field of nonlinear waves is an exciting area of modern mathematical research that also plays a major role in many application areas from physics and fluids. The articles in this volume present a diverse cross section of topics from this field including work on the Inverse Scattering Transform, scattering theory, inverse problems, numerical methods for dispersive wave equations, and analytic and computational methods for free boundary problems. Significant attention to applications is also given throughout the articles with an extensive presentation on new results in the free surface problem in fluids. This volume will be useful to students and researchers interested in learning current techniques in studying nonlinear dispersive systems from both the integrable systems and computational points of view.

Issues in General and Specialized Mathematics Research: 2011 Edition

Issues in General and Specialized Mathematics Research: 2011 Edition
Author:
Publisher: ScholarlyEditions
Total Pages: 1326
Release: 2012-01-09
Genre: Mathematics
ISBN: 1464964920

Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Shaping Light in Nonlinear Optical Fibers

Shaping Light in Nonlinear Optical Fibers
Author: Sonia Boscolo
Publisher: John Wiley & Sons
Total Pages: 522
Release: 2017-03-08
Genre: Technology & Engineering
ISBN: 1119088143

This book is a contemporary overview of selected topics in fiber optics. It focuses on the latest research results on light wave manipulation using nonlinear optical fibers, with the aim of capturing some of the most innovative developments on this topic. The book’s scope covers both fundamentals and applications from both theoretical and experimental perspectives, with topics including linear and nonlinear effects, pulse propagation phenomena and pulse shaping, solitons and rogue waves, novel optical fibers, supercontinuum generation, polarization management, optical signal processing, fiber lasers, optical wave turbulence, light propagation in disordered fiber media, and slow and fast light. With contributions from leading-edge scientists in the field of nonlinear photonics and fiber optics, they offer an overview of the latest advances in their own research area. The listing of recent research papers at the end of each chapter is useful for researchers using the book as a reference. As the book addresses fundamental and practical photonics problems, it will also be of interest to, and benefit, broader academic communities, including areas such as nonlinear science, applied mathematics and physics, and optical engineering. It offers the reader a wide and critical overview of the state-of-the-art within this practical – as well as fundamentally important and interesting – area of modern science, providing a useful reference which will encourage further research and advances in the field.

Recent Advances in Nonlinear Partial Differential Equations and Applications

Recent Advances in Nonlinear Partial Differential Equations and Applications
Author: Luis López Bonilla
Publisher: American Mathematical Soc.
Total Pages: 250
Release: 2007
Genre: Mathematics
ISBN: 0821842110

The articles of this book are written by leading experts in partial differential equations and their applications, who present overviews here of recent advances in this broad area of mathematics. The formation of shocks in fluids, modern numerical computation of turbulence, the breaking of the Einstein equations in a vacuum, the dynamics of defects in crystals, effects due to entropy in hyperbolic conservation laws, the Navier-Stokes and other limits of the Boltzmann equation, occupancy times for Brownian motion in a two dimensional wedge, and new methods of analyzing and solving integrable systems are some of this volume's subjects. The reader will find an exposition of important advances without a lot of technicalities and with an emphasis on the basic ideas of this field.

Handbook of Dynamical Systems

Handbook of Dynamical Systems
Author: B. Fiedler
Publisher: Gulf Professional Publishing
Total Pages: 1099
Release: 2002-02-21
Genre: Science
ISBN: 0080532845

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to namejust a few, are ubiquitous dynamical concepts throughout the articles.

Integrable Systems and Random Matrices

Integrable Systems and Random Matrices
Author: Jinho Baik
Publisher: American Mathematical Soc.
Total Pages: 448
Release: 2008
Genre: Mathematics
ISBN: 0821842404

This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.

Issues in Applied Mathematics: 2011 Edition

Issues in Applied Mathematics: 2011 Edition
Author:
Publisher: ScholarlyEditions
Total Pages: 864
Release: 2012-01-09
Genre: Mathematics
ISBN: 1464965064

Issues in Applied Mathematics / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Applied Mathematics. The editors have built Issues in Applied Mathematics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Applied Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.