OSCILLATING WAVES ARISING FROM O(2) SYMMETRY

In the problems with O(2) symmetry, the Jacobian matrix at the branch of nontrivial Z(2) symmetric steady-state solutions always has a zero eigenvalue due to the group orbit of solutions. Hopf bifurcation has b een considered where a pair of complex eigenvalues also crosses the im aginary axis. Canonical coordinates have been used to remove the degen eracy of the system, The bifurcating branch has a particular type of s patio-temporal symmetry which can be broken in a further bifurcation g iving rise to modulated travelling wave solutions which drift round th e group orbit, (C) 1997 Elsevier Science B,V.