About the mechanism of switching between standing and traveling waves is accompanied by a halving of the wavelength

We suggest a possible mechanism for the transition from standing waves with a wavelength $\lambda_{SW}$ to traveling waves with a half wavelength: $\lambda_{TW} \cong \lambda_{SW}/2$. This phenomenon was observed inthe Belousov–Zhabotinsky reaction dispersed in a water-in-oil aerosol OT/Span-20 microemulsion. The problem is solved in a spatially one-dimensional case using amplitude equations approach. We demonstrate that a transition is possible under certain conditions. We obtain conditions for the mode coupling strength parameters, under which the scenario of transition from a standing wave to a half-period traveling wave, observed experimentally, is realized. The result of theoretical analysis is confirmed by numerical simulations.