2017 Participating school in analysis of PDE

                        Stability of solitons and periodic waves

Organizers: Mathew Johnson, Masaya Maeda, Tetsu Mizumachi, and Soonsik Kwon(local)


The participating school is an intensive reading seminar. The goal is to learn about important recent progress in analysis and PDE. We choose a subject which has shown great progress in recent years and select a series of breakthrough works for discussion. The organizers will give lectures providing background and context for these works.  Each participant will presents one topic in two lectures. The main targets are graduate students and young researchers working in the area of analysis.  Experienced researchers who are interested in this topic are also welcome. The school is supported by CMC at KAIST

Dates:   Aug 21(Mon) ~ 25(Fri), 2017 (arrive on 20th, depart on 26th).

Location: KAIST, Daejeon, Korea.

List of topics 

  1. Y. Martel, and F. Merle, Asymptotic stability of solitons of the subcritical gKdV equations revisited, Nonlinearity 18 (2005), 55-80.        Presenter: Taeseok Lee  slide
  2. R. Pego, and M.I Weinstein, Asymptotic Stability of Solitary Waves, Comm. Math. Phys. 164 (1994), 305-349.         Presenter: Haewon Yoon slide
  3. Y. Martel, F. Merle, and T.-P. Tsai, Stability and Asymptotic Stability in the Energy Space of the Sum of N Solitons for Subcritical gKdV Equations, Comm. Math. Phys. 231 (2002), 347-373.      Presenter: Noriyoshi Fukaya  note
  4. D. Bambusi, and S. Cuccagna, On dispersion of small energy solutions of the nonlinear Klein Gordon equation with a potential, Amer. J. Math. 133(2011)  no.5, 1421–1468.           Presenter: Kihyun Kim,  Ikkei Shimizu .  Instruction_BC11AJM       slide(Shimizu)    note(Kim)
  5. A. Soffer, and M. I. Weinstein, Multichannel Nonlinear Scattering for Nonintegrable Equations, Comm. Math. Phys. 133 (1990), 119-146.          Presenter : Chulkwang Kwak   Instruction_SW90CMP       slide1 slide2
  6. B. Barker, M. Johnson, P. Noble, L. M. Rodrigues, K. Zumbrun, Nonlinear Modulational Stability of Periodic Traveling-Wave Solutions of the Generalized Kuramoto-Sivashinsky Equation.       Presenter : Sekisaka Ayuki   part1  part2
  7. M. Johnson, P. Noble, L. M. Rodrigues, K. Zumbrun, Non-localized Modulation of periodic reaction diffusion waves: Nonlinear stability, Arch. Rat. Mech. Anal. 207 (2013) 669–692.        Presenter :  Soyoun Jung  slide
  8. J. Bronski, V. Hur, and M. Johnson, Modulational Instability in Equations of KdV Type, Chapter 4, New approaches to nonlinear waves, Lecture notes in Physics, Springer 2016.           Presenter : Juinichi Harada            Instruction of 6,7,8    note

Johnson’s lecture note on Basic Stability Theory



Space is limited. As we will discuss 8 topics this year, we expect slightly more than 10 spaces are available.

Typical participants will be graduate students, postdoc, or young researchers working near the field. They need not be expertised in the subject. If you are interested in participation, please write a short email to Soonsik Kwon soonsikk@kaist.edu by May 30. In your email, describe your academic status, field of interest, and motivation to participate. Also, if you are a Ph.D., attach your CV, or if you are a graduate student, then let your advisor write a short email on his/her dissertation topic.

CMC supports local expense including accommodation and meals for all participants. However, we ask participants to arrange their travel grant from other sources.


Instruction to participants

Each participant will give two talks of length 50 min on a single paper. Organizers will assign topics(=paper) to present to each participant, according to their preference list. Participants will submit a summary note if you will give blackboard talk or  slide file, if you will give slide talk, by two weeks before the meeting.

In the meeting, we will hand out a printout of notes and slides. We highly recommend participants to take a look at most of articles in the list before the meeting and bring them to the meeting. If you don’t have access to any of those papers in the list from your affiliation, then please ask organizers.