Stability of travelling waves. (English) Zbl 0885.34039
Summary: An extended system was introduced in [P. J. Aston, A. Spence and W. Wu, SIAM J. Appl. Math. 52, No. 3, 792-809 (1992; Zbl 0764.34033)] for the computation of travelling wave (or rotating wave) solutions of nonlinear ODE’s with \(O(2)\) symmetry. We show that the stability of the travelling waves can be determined by the eigenvalues of the extended system in a way similar to the situation for the stability of usual steady-state solutions.
MSC:
34C25 | Periodic solutions to ordinary differential equations |
34D30 | Structural stability and analogous concepts of solutions to ordinary differential equations |