**Contemporary Mathematics**

Volume: 635;
2015;
210 pp;
Softcover

MSC: Primary 35; 47; 37; 65;

Print ISBN: 978-1-4704-1050-6

Product Code: CONM/635

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

**Electronic ISBN: 978-1-4704-2274-5
Product Code: CONM/635.E**

List Price: $105.00

AMS Member Price: $84.00

MAA Member Price: $94.50

# Nonlinear Wave Equations: Analytic and Computational Techniques

Share this page *Edited by *
*Christopher W. Curtis; Anton Dzhamay; Willy A. Hereman; Barbara Prinari*

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.

#### Readership

Graduate students and research mathematicians interested in nonlinear wave equations and applications.

# Table of Contents

## Nonlinear Wave Equations: Analytic and Computational Techniques

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Recurrence in the Korteweg-de Vries equation? 114 free
- On the Location of the Discrete Eigenvalues for Defocusing Zakharov-Shabat Systems having Potentials with Nonvanishing Boundary Conditions 1326
- The Novikov-Veselov Equation:Theory and Computation 2538
- Transverse instability of plane wave soliton solutions of the Novikov-Veselov equation 7184
- 1. Introduction 7184
- 2. From planar solutions of Novikov–Veselov to KdV 7386
- 3. A Pseudo-Spectral method for the solution of (2+1) nonlinear wave equations 7588
- 4. Instability of traveling-wave solutions of the NV-equation to transverse perturbations 7992
- 5. Numerical Results on the Instabilities of Plane-Wave Soliton Solutions 8497
- 6. Conclusions 87100
- References 87100

- Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation: Recent developments 91104
- Relative-Periodic Elastic Collisions of Water Waves 109122
- The Instabilities of Periodic Traveling Water Waves with Respect to Transverse Perturbations 131144
- Relationships between the pressure and the free surface independent of the wave-speed 157170
- Comparison of Five Methods of Computing the Dirichlet–Neumann Operator for the Water Wave Problem 175188
- Back Cover Back Cover1226