The stability of coherent structures and patterns

June 11-12, 2012

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

The transverse instability growth rates of the NLS soliton.

The evolution of the phase of a perturbed stationary solution of the NLS
equation with periodic potential.

A picture of a storm caused by Hurricane Grace, the Halloween Storm of 1991.

Organizing Committee:

John Carter (Mathematics, Seattle University)
Bernard Deconinck (Applied Mathematics, University of Washington)
J. Nathan Kutz (Applied Mathematics, University of Washington)
Bjorn Sandstede (Applied Mathematics, Brown University)
Michael J. Ward (Mathematics, University of British Columbia)

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 three 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 3 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.

Course 1. An introduction to stability analysis
Lecturer: Margaret Beck (Mathematics, Boston University and Heriot-Watt University, 4 lectures)
Course 2. Using AUTO for stability problems.
Lecturer: Bjorn Sandstede (Mathematics, Brown University), assisted by David Lloyd (Surrey University) (4 lectures, tutorial files)

Please visit and follow the instructions there prior to the workshop.

Course 3: Nonlinear and orbital stability.
Lecturer: Walter Strauss (Mathematics, Brown University, 4 lectures)

Participation and support

The workshop is specifically aimed at graduate students and beginning researchers, although others are invited to participate as well. Limited funding is available to students and postdoctoral fellows, through generous support of the the National Science Foundation and the Pacific Institute for the Mathematical Sciences.
- 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 Registration is currently closed.
- Support for students. We intend to provide qualified students up to US$400 for the cost of airfare or driving, and lodging. 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 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, and depends on funding availability.
- Support for postdoctoral fellows. We intend to reimburse postdoctoral researchers up to US$300 for participating in the workshop, which should cover the incremental cost of attending the workshop if they are attending the SIAM Conference. To apply for support, please send e-mail to 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, and depends on funding availability.


This is a short, but intensive workshop. The full two days will be used, starting early on Monday, ending late on Tuesday.

Monday 6/11
Guggenheim Hall 220
Tuesay 6/12
Sieg Hall 134
9:00-9:50 Introduction 1: Margaret Beck Introduction 4: Margaret Beck
10:00-10:30 Break Break
10:30-11:20 Introduction 2: Margaret Beck Nonlinear Stability 2: Walter Strauss
11:30-12:20 AUTO and Stability 1: Bjorn Sandstede AUTO and Stability 3: Bjorn Sandstede
12:30-14:00 Lunch Lunch
14:00-14:50 AUTO and Stability 2: Bjorn Sandstede AUTO and Stability 4: Bjorn Sandstede
15:00-15:50 Introduction 3: Margaret Beck Nonlinear Stability 3: Walter Strauss
16:00-16:30 Break Break
16:30-17:20 Nonlinear Stability 1: Walter Strauss Nonlinear Stability 4: Walter Strauss
17:30-19:30 Dinner, Reception

As noted above: Bjorn Sandstede will be assisted by David Lloyd.

Lecture notes

Lecture notes are linked to above.

Lodging, transportation and local information

Lodging options are found here. Note that the Hotel Deca is the conference hotel for the SIAM conference. More information is available from Lodging, transportation, etc.. Participants are encouraged to arrange for room sharing.

All lectures will be in Guggenheim Hall on the University of Washington Campus.

2006 Workshop

The lecture notes from the 2006 Workshop remain available:
Course 1. An introduction to stability analysis
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 )