The global bifurcation and geometric properties of steady periodic equatorial internal waves with fixed-depth

Abstract

In this paper, we mainly consider steady periodic equatorial internal waves with a fixed mean depth d>0. By extending the local bifurcation curve obtained in [1], we prove the existence of equatorial internal waves of large amplitude, where the analytic bifurcation theorem and analysis of nodal patterns play a key role. Furthermore, we also obtain some important geometric properties on equatorial internal waves, including the concavity and convexity and symmetry of wave profile.