Two codes for the numerical solution of ODEs by John Polking
of Rice University are:
pplane7.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.
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 solitary wave
Some papers on MI:
The 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 recent preprint together with Lars English
and his website on discrete solitons
The paper that Prof. Whitaker will be talking about in his guest lecture
on two-component discrete NLS equations
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 connection to integrability
and in affecting the phenomenology of kink collisions
A few introductory links for Matlab:
A basic tutorial for Matlab
A Matlab Tutorial by Peter Turner of Clarkson University
An online tutorial by Mathworks
A
Matlab Tutorial by Monica Nitsche of the University of New Mexico
Additional Links:
An interesting applet site suggested by Steve Sarasin
An interesting soliton site with animations created by Abhinav Guliani
