Abstract
In this paper, we apply the bifurcation theory to study the steady two-dimensional periodic equatorial water waves for the f-plane approximation. We consider the waves with vorticity which propagate with a specified fixed depth between the thermocline and the upper boundary of the centre layer. Moreover, we present a functional J and its first variation corresponds to the exact equations in the transformed variables. Using the second variation of J, we prove a formal stability result for the bifurcation inducing the laminar solution.
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