This repository holds the Matlab/Octave scripts which were used in the in-slice integration of the Kuramoto-Sivashinsky system in Budanur et al. (2014).
In order to test the code on your system, start a Matlab or Octave
instance in ffmSice/scripts/ and run ks_statesp_red or
ks_statesp_full. When runs, ks_statesp_red and ks_statesp_full
produces Matlab/Octave-equivalents of Figure 2 b and Figure 2 a of
Budanur et al. (2014) respectively.
Octave 3.8.1, and Matlab R2013b
ffmSlice/scripts/
-
Lg.m: SO(2) generator -
LieEl.m: SO(2) element -
SliceCond.m: Slice condition -
slicep.m: Slice fixing point (0,1,0,0,...) -
vel.m: Velocity function in real representation -
vksred.m: Reduced velocity function in real representation -
gradV.m: KS stability matrix in real representation -
gradVred.m: KS reduced stability matrix -
ksETDRK4.m: KS solver in full state space -
ksETDRK4red.m: KS solver in the first-mode slice -
ks_statesp_red.m: Computes the unstable manifold of TW_1 on the first Fourie mode slice, and plots it on a state space projection along with TW_2, and RPO_{33.50} (arXiv: 1405.1096, Fig 2.b). -
ks_statesp_full.m: Same withks_statesp_red.m, but trajectories are computed in the full state space, in addition, group orbits of TW_1 and TW_2 are drawn (arXiv: 1405.1096, Fig 2.a).
ffmSlice/docs/
-
docSlice.tex: Latex document which explains implementation details of the in-slice integration of Kuramoto-Sivashinsky system.
pdflatex docSlice -
def.tex: Definitions used in
docSlice.tex
MIT license
Copyright (c) 2014 Nazmi Burak Budanur, http://cns.physics.gatech.edu/~burak