Equivariant cosymmetry and front solutions of the Dubreil-Jacotin-Long equation. Part 2: Exact solutions

The paper concerns existence of exact solutions of the Dubreil-Jacotin-Long equation describing large amplitude internal fronts in a continuously stratified fluid. The proof uses cosymmetric variant of the implicit function theorem based on the group invariance of the variational functional for DJL operator. Supercritical branching occurs near approximate front solutions at the boundary of continuous spectrum of the problem linearized with respect to the basic uniform flow.