Lecturer:Panos Kevrekidis
Class Meetings:TTh 11:30-12:45, LGRT 143
PK's Office Hours: W 12:00-2:00 p.m., Th: 1:00-2:30 p.m., or by appointment.
PK's Contact Info:
Office:LGRT 1524
E-mail: kevrekid@math.umass.edu
Mailbox:LGRT 1623D


General Information Handout

Project Suggestions


Assignment 1: Due Thursday, February 1

Assignment 2 : Due Tuesday, February 13

Assignment 3 : Due Tuesday, February 27

Assignment 4 : Due Thursday, March 8

Assignment 5 : Due Tuesday, March 27

Assignment 6 : Due Thursday, April 5

Assignment 7 : Due Thursday, April 19

Assignment 8 : Due Tuesday, May 1

Downloads / Matlab Computations:

Two codes for the numerical solution of ODEs by

John Polking

of Rice University are:

pplane8.m for planar systems

odesolve.m for higher-order autonomous systems

T. Dauxois' et al. code for FPU


the function it calls

Some papers on FPU:

The original FPU paper


the nice expository paper by Dauxois, Peyrard and Ruffo

as well as an interesting

historical note.

The current state of the art on the FPU problem

Codes for KdV:

A code in the spirit of the original soliton paper by Zabusky and Kruskal


a more modern (spectral) one for soliton interactions by Nick Trefethen

Here is the original KdV paper of Zabusky and Kruskal. Codes for NLS:

A code showing modulational instability of a low wavenumber


one showing the stable propagation of a solitary wave

Some papers on MI:

The more recent account of Zakharov-Ostrovsky


the use of MI to get solitary waves in BECs

as well as a

theoretical analysis of MI in BECs.

A couple of papers on the EP equation:

The geometric derivation of its solutions


its use in scalar field cosmologies.

A couple of sites discussing the Jacobi elliptic functions:

One from Wikipedia


one from MathWorld.

A site on Dispersive Shock Waves

from Scholarpedia

A recent paper on the diffusion equation

explaining its self-similar solutions

A couple of sites/works discussing the coupled torsion pendula:

A paper involving also experiments from Lars English


his website on discrete solitons

The very interesting paper of Goodman and Haberman on

kink-antikink collisions

A simple code for a

Newton iteration of the ``nonlinear'' equation exp(x)=1

A couple of codes for the discrete sine-Gordon:

A code performing a Newton-based continuation of the unstable kink


one integrating the result to showcase the relevant instability

An interesting discussion of Noether theory for both individual degrees of freedom, as well as for fields from


A couple of references regarding the role of internal modes

in affecting the phenomenology of kink collisions


in connection to integrability

A few introductory links for Matlab:

Some tutorials for Matlab

A Matlab Tutorial by Peter Turner of Clarkson University

A Matlab Tutorial by Monica Nitsche of the University of New Mexico

Additional Links:

An interesting applet site for Wave Phenomena