Back MatterSource: SIAM Review, Vol. 27, No. 1 (Mar., 1985)Published by: Society for Industrial and Applied MathematicsStable URL: http://www.jstor.org/stable/2031532 .

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ANDTHE ~~~~~04

TRANSFORM by M. J. Ablowitz 12

and H. Segur

Here is a complete exposition of the inverse scattering transform and its application to problems of nonlinear dispersive waves. The theory provides a rich spectrum of new ideas in mathematics with interesting results in differential geometry, analytic function theory, algebraic geometry, partial and ordinary differential equations, difference equations, and integral equations.

This book contains a broad selection of material relating to what is commonly called "soliton theory"; it serves not only as an introduction and foundation for studying the inverse scattering transform, but also as a treatise on the subject. It introduces the reader to solitons and the inverse scattering transform, brings the reader to the forefront of current research, and simultaneously provides a suitable text for graduate students.

Ablowitz and Segur have been working in the area of nonlinear waves and soliton theory for almost fifteen years. Collectively, they have written more than 75 research papers, a number of which are considered to be seminal papers in the field. They have been principal lecturers at numerous national and international conferences. Mark Ablowitz received his Ph.D. in mathematics from Massachusetts Institute of Technology in 1971. He is currently chairman of the mathematics department of Clarkson College. Harvey Segur received his Ph.D. in mechanical engineering from the University of California at Berkeley. He joined the mathematics department at Clarkson College in 1971, after a postdoctoral appointment in applied mathematics at California Institute of Technology. He is senior consultant at Aeronautical Research Associates of Princeton.

$57.00 list, $45.60 SIAM member 1981, x + 425 pp.

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Fourier Analysis ' = of Numerical A

Approximaftons of VCr Hyperbolic Equations 16h

by R. Vichnevetsky and J. B. Bowles /l J efV'

There has been renewed interest over the past decade in the use of Fourier analysis to examine questions of accuracy and stability of numerical methods for solving partial differential equations. This kind of analysis can produce particularly attractive and useful results for hyperbolic equations. Most results of this character were discovered during the 1970's. It is largely to these recent results that the authors devote their attention.

The authors concentrate on the errors of various finite difference and finite element discretizations of linear, constant coefficient hyperbolic equations using Fourier methods. Their approach provides many insights to the stability of discretizations as well as to dispersion, damping, etc. Such information can be very useful to users of numerical methods because its qualitative implications often carry over to the more complicated practical problems involving nonlinear hyperbolic equations.

The book is a useful reference for those working with computers in the analysis of problems in such diverse fields as hydraulics, gas dynamics, plasma physics, numerical weather prediction, and transport processes in engineering who need to understand the implications of the approximations they use, and for applied mathematicians concerned with the more theoretical aspects of these computations.

Contents: Introduction El Fourier analysis of the accuracy of semi-discretizations El Higher order semi-discretizations El Full discretizations LI Damping. diffusion and filtering El Group velocity LI Time-Fourier transforms LI Fourier analysis and L2-norm of the global error LI Spectral methods Oi Equations in two dimensions: anisotropy El Bibliography El Index

1982, xii + 140 pp. $23.00/list, $18.40/SIAM member

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.45VR bIMARCH * 1985 VOLUME 27 NUMBER 1

A PUBLICATION OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS

CONTENTS ARTICLES Decoupling and Stability of Algorithms for Boundary Value Problems .................. R. M. M. Mattheij I Pattern Generation in Space and Aspect ............................... Simon A. Levin and Lee A. Segel 45

CLASSROOM NOTES IN APPLIED MATHEMATICS A Simple Proof that the World is Three-Dimensional ..................................... Tom Morley 69 Poisson Processes and a Bessel Function Integral ........................................ F W Steutel 73

PROBLEMS Modes of a Random Variable ..................................................... A. N. Philippou 79 Incidence Matrix for a Transportation Problem ......................................... S. W. Wallace 79 A Limit of Bernstein Polynomials ...................................................... G. Chang 80 An Asymptotic Problem ........................................................ Pierre Barrucand 80 Pendulum in a Variable Medium ................................................. M. A. Abdelkader 80

SOLUTIONS Factorization of a Homogeneous Polynomial (A. M. Gleason) ............................ A. M. Gleason 80 An Integral on S0(3) (B. E. Eichinger) ............................................ Donald Richards 81 Zeros of a Definite Integral (Tian Jinghuang) ................................................ (open) 82 A Nonlinear Differential Equation (M. A. Abdelkader) ................................. A. D. Osborne 83 A Definite Integral (B. C. Berndt) ................................... W E. Hornor and C C Rousseau 84 A Vanishing Definite Integral (M. L. Glasser) .............................................. (closed) 85

BOOK REVIEWS Stochastic Models in Operations Research, Volume II. Stochastic Optimization. (Daniel P Heyman and Matthew

J. Sobel) ........................................................ Jeffrey L. Arthur 87 Computers in Chess-Solving Inexact Search Problems (M. M. Botvinnik) .................. Hans Berliner 88 Catastrophe Theory (V. I. Arnold) .............................................. Stephen R. Bernfeld 90 Linear Programming (Katta G. Murty) and Linear Programming (Vasek Chvatal) ............. Charles Blair 91 Primer of Modern Analysis (Kennan T. Smith) ........................................... R. P Boas 93 Asymptotic Treatment of Chemically Reacting Systems (Ashwani K. Kapila) .............. John Buckmaster 94 Geometrical Methods in the Theory of Ordinary Differential Equations (V. I. Arnold) ........ Charles Conley 95 Partial Differential Equations of Applied Mathematics (Erich Zauderer) .................. John W Dettman 96 The Mathematical Theory of Black Holes (S. Chandrasekhar) ............................. Bryce DeWitt 97 Kinematics (Joseph Stiles Beggs) .................................................... Joseph Duffy 99 Introductory Applied Probability (G. P. Beaumont) ....................................... Meyer Dwass 100 Optimization Over Time-Volume II: Dynamic Programming and Stochastic Control (Peter Whittle)

Robert J. Elliott 100 Hamilton-Jacobi Equations in Hilbert Spaces (V. Barbu and G. DaPrato) ............... Lawrence C Evans 101 Scattering Theory for Many-Body Quantum Mechanical Systems-Rigorous Results (Israel Michael Sigal)

George A. Hagedorn 103 Optimal Processes on Manifolds (Roel Nottrot) ..................................... William W. Hager 104 Volterra Integral and Differential Equations (T. A. Burton) ......................... Kenneth B. Hannsgen 104 Variational Methods in Theoretical Mechanics (J. T. Oden and J. N. Reddy) ............... Edward J. Haug 105 The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Colin Sparrow) .......... Philip Holmes 106 Probability (A. N. Shiryayev) ................................................. J. H. B. Kemperman 110 A First Course in the Mathematical Foundations of Thermodynamics (David R. Owen) ........ Joseph Kestin 110 The Unix System Guidebook: An Introductory Guide for Serious Users (Peter P Silvester)

M. S. Krishnamoorthy 113 Introduction to Sensitivity and Stability Analysis in Nonlinear Programming (Anthony V. Fiacco). .C E. Lemke 114 Bifurcation Theory, Mechanics and Physics (C. P. Bruter, A. Aragnol and A. Lichnerowicz, editors)

Jerry Marsden 116 Identification of Continuous Dynamical Systems-The Poisson Moment Functional (PMF) Approach (Dines Chandra

Saha and Ganti Prasada Rao) ............................................. Richard E. Mortensen 116 Numerical Methods in Heat Transfer (R. W. Lewis, K. Morgan and B. A. Schreifler, editors) Chander Prakash 118 First Order Elliptic Systems: A Function Theoretic Approach (Robert P. Gilbert and James L. Buchanan)

M. H. Protter 119 Introduction to Dynamics (Ian Percival and Derek Richards) ............................. Joel W Robbin 121 An Introduction to Convex Polytopes (Arne Brondsted) ................................... G. T Sallee 123 Stochastic Transport in Discrete Biological Systems (Eckhart Frehland) .................... Stanley Sawyer 124 Solitons (P. G. Drazin) .............................................................. Alwyn Scott 125 Non-Equilibrium Entropy and Irreversibility (G. Lindblad) .............................. Herbert Spohn 125 Studies in Applied Mathematics (Victor Guillemin, editor) ............................. A. S. Wightman 127 Nonlinear Programming (Garth P. McCormick) .................................... Jean-Phillippe Vial 128 Algebraic Theory for Multivariable Linear Systems (H. Blomberg and R. Ylinen) .......... Stanislaw H. Zak 130 Constrained Optimization and Lagrange Multiplier Rules (Dimitri P. Bertsekas) .................. S. Zlobec 131

CHRONICLE New Members .139 Elected and Appointed Off icias.148

CODEN: SIREAD

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