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
Phone:413-577-1977
Fax:413-545-1801
E-mail: kevrekid@math.umass.edu
Mailbox:LGRT 1623D

Handouts:

General Information Handout

Project Suggestions


Assignments:

Assignment 1: Due Thursday, February 1

Assignment 2 : Due Tuesday, February 13

Assignment 3 : Due Tuesday, February 27

Assignment 4 : Due Thursday, March 8


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

and

the function it calls

Some papers on FPU:

The original FPU paper

and

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

and

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

and

one showing the stable propagation of a solitary wave

Some papers on MI:

The more recent account of Zakharov-Ostrovsky

and

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

and

its use in scalar field cosmologies.

A couple of sites discussing the Jacobi elliptic functions:

One from Wikipedia

and

one from MathWorld.

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

A paper involving also experiments from Lars English

and

his website on discrete solitons

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

and

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

Wikipedia

A couple of references regarding the role of internal modes

in affecting the phenomenology of kink collisions

and

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