Workshop
Stability and instability of nonlinear waves

September 6-8, 2006; University of Washington; Seattle, Washington
Hosted by The Department of Applied Mathematics

Supported by the National Science Foundation and the Pacific Institute for the Mathematical Sciences

A picture of a storm caused by Hurricane Grace, the Halloween Storm of 1991. The evolution of the phase of a perturbed stationary solution of the NLS equation with periodic potential. A genus 3 solution of the KP equation

Organizing Committee:

 Bernard Deconinck (Applied Mathematics, University of Washington)
J. Nathan Kutz (Applied Mathematics, University of Washington)
John Stockie (Mathematics, Simon Fraser University)
e-mail: stability@amath.washington.edu

Related conference: SIAM Conference on Nonlinear Waves and Coherent Structures


Scientific objectives and scope

Stability plays an essential role in many branches of science and engineering, including several aspects of fluid mechanics, high-speed transmission of information, and feasibility of MHD fusion devices. The objective of the workshop is to give an overview of current state-of-the-art methods for examining stability, as well as to present some widely applicable new techniques. The format will consist of four invited speakers giving a series of lectures at a level aimed at graduate students but useful for researchers from a variety of disciplines, such as mathematics, engineering, biology, etc.

Workshop description

Although the topic of stability of solutions of partial differential equations is important in almost any application area, the most powerful techniques one uses to examine stability are hardly ever taught in courses. This is mainly because many of these techniques have come about fairly recently. We are organizing a workshop where these techniques are taught in 4 mini-courses. The workshop is aimed at graduate students, postdoctoral fellows and young researchers interested in stability methods, working in different disciplines on a variety of applications.

A detailed description of workshop topics is available here. This list may change.

Course 1. An introduction to stability analysis of nonlinear waves.
Lecturer: Mariana Haragus (Mathematics, U. de Franche-Comte) (4 lectures)
Course 2. The Evans function.
Lecturer: Todd Kapitula (Mathematics and Statistics, U. of New Mexico) (4 lectures)
Course 3. Numerical methods.
Lecturers: J. Nathan Kutz (Applied Mathematics, U. of Washington) (1 lecture), Bernard Deconinck (Applied Mathematics, U. of Washington) (1 lecture), Jens Rademacher (Weierstrass Institute, Berlin) (1 lecture), Jeff Humpherys (Mathematics, Brigham Young) (1 lecture)
Course 4: Nonlinear stability.
Lecturer: Harvey Segur (Applied Mathematics, U. of Colorado, Boulder) ( lecture 1, lecture 2, lecture 3, lecture 4 )

Participation and support

A list of confirmed participants is found here.

The workshop is specifically aimed at graduate students and beginning researchers. Support is available for graduate students and postdoctoral fellows, although others are invited to participate as well. This is made possible by generous contributions from the National Science Foundation Mathematical Sciences VIGRE grant at the University of Washington, and the Pacific Institute for the Mathematical Sciences. Support is not restricted to US or Canadian nationals or residents. Students and postdoctoral fellows from elsewhere are also encouraged to attend and to apply for support.

- Registration. There is no registration fee, but all have to register to attend, so we may estimate required classroom size, and quantity of refreshments. To register, e-mail your intent to do so to stability@amath.washington.edu
- Support for students. We intend to provide qualified students with US$400 for the cost of airfare and lodging. Graduate students who are considered local and are driving to the workshop will be reimbursed US$200. Participating students are highly encouraged to participate in the SIAM Conference on nonlinear waves and coherent structures, for instance by presenting a poster or a contributed talk. To apply for support, please send e-mail to stability@amath.washington.edu with a description of your status and research, who your advisor is, and your motivation for wanting to participate in the workshop. Support is available to qualified candidates on a first-come, first-serve basis.
- Support for postdoctoral fellows. We intend to reimburse postdoctoral researchers US$300 for participating in the workshop, which should more than cover the incremental cost of attending the workshop if they are attending the SIAM Conference. To apply for support, please send e-mail to stability@amath.washington.edu with a description of your status and research, and your motivation for wanting to participate in the workshop. Support is available to qualified candidates on a first-come, first-serve basis.
At the moment, we have exhausted our funding for participants. However, it is possible that funding will become available as some participants cancel.

Schedule

Wednesday, 9/6/06 Thursday, 9/7/06 Friday, 9/8/06
08.45-9.00 Introductory comments
09.00-10.00 Introduction I Introduction III Numerics III
10.00-11.00 Introduction II Introduction IV Numerics IV
11.00-11.30 Break Break Break
11.30-12.30 Numerics I Evans III Nonlinear III
12.30-14.00 Lunch Lunch Lunch
14.00-15.00 Evans I Evans IV Nonlinear IV
15.00-16.00 Evans II Nonlinear I
16.00-16.30 Break Break Discussion I (15.30-16.30)
16.30-17.30 Numerics II Nonlinear II Discussion II

All lectures and the discussion session will be in Condon Hall 109. In addition, we are having a post-workshop party, friday at 6pm in the Sylvan theatre, next to the Paul G. Allen Center for Computer Science and Engineering

Lecture notes

All lecturers have agreed to provide lecture notes. When possible these notes will be made available to the participants. We intend to edit and publish these lecture notes to ensure continued availability of this material, presented at a level suitable for graduate students. This volume could be the starting point for anyone interested in stability of nonlinear waves.

Lodging, transportation and local information

We recommend any one of the Best Western University Tower Hotel, the College Inn, the University Inn, the University Motel or the Watertown Hotel for lodging, because of proximity to the workshop location. Note that the Best Western University Tower Hotel is the conference hotel for the SIAM conference. More information is available from Lodging, transportation, etc.. Participants are encouraged to arrange for room sharing.

Department of Applied Mathematics