Nonlinear Wave Equations: Analytic and Computational Techniques
About this Title
Christopher W. Curtis, San Diego State University, San Diego, CA, Anton Dzhamay, University of Northern Colorado, Greeley, CO, Willy A. Hereman, Colorado School of Mines, Golden, CO and Barbara Prinari, University of Colorado, Colorado Springs, Colorado Springs, CO, Editors
Publication: Contemporary Mathematics
Publication Year 2015: Volume 635
ISBNs: 978-1-4704-1050-6 (print); 978-1-4704-2274-5 (online)
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.
Graduate students and research mathematicians interested in nonlinear wave equations and applications.
Table of Contents
- Ben Herbst, Garrett Nieddu and A. David Trubatch – Recurrence in the Korteweg-de Vries equation?
- F. Demontis, C. van der Mee and F. Vitale – On the Location of the Discrete Eigenvalues for Defocusing Zakharov-Shabat Systems having Potentials with Nonvanishing Boundary Conditions
- R. Croke, J. L. Mueller, M. Music, P. Perry, S. Siltanen and A. Stahel – The Novikov-Veselov Equation:Theory and Computation
- Ryan Croke, Jennifer L. Mueller and Andreas Stahel – Transverse instability of plane wave soliton solutions of the Novikov-Veselov equation
- Gregory D. Lyng – Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation: Recent developments
- Jon Wilkening – Relative-Periodic Elastic Collisions of Water Waves
- Katie Oliveras and Bernard Deconinck – The Instabilities of Periodic Traveling Water Waves with Respect to Transverse Perturbations
- Katie Oliveras and Vishal Vasan – Relationships between the pressure and the free surface independent of the wave-speed
- Jon Wilkening and Vishal Vasan – Comparison of Five Methods of Computing the Dirichlet–Neumann Operator for the Water Wave Problem