Abstract
The equatorial waveguide in the vicinity of the Earth equator in the ocean and atmosphere is a semi-transparent one since the systems contain both the wave modes trapped in this waveguide and the free modes freely propagating across the equator. Non-linear interactions between the trapped and free Rossby waves are studied using two-layer model of the ocean, or the atmosphere. It is shown that the free wave can resonantly excite a pair of the trapped ones with amplitudes much greater than its proper amplitude. In turn, the interaction between the excited trapped modes results in a non-linear scattering of the free wave on the wave guide. The envelopes of the baroclinic waves obey Gmzburg-Landau type equations and exhibit non-linear saturation and formation of characteristic "domain wall" and "dark soliton" defects.
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