Variational Nonlinearities and Wave Selection at an $O(2)$-Hopf Bifurcation

At an $O(2)$-equivariant Hopf bifurcation, the real parts $ζ_R$ and $ξ_R$ of the two cubic normal-form coefficients govern selection between traveling and standing waves. In a fourth-order regularized $p$-system, $ξ_R$ was observed to vanish and the cubic nonlinearity to shift only frequencies. We s