Edward Huynh and Keoni Castellano (both Mathematical Sciences) recently published their work, "Remarks on the Preservation and Breaking of Translational Symmetry for a Class of ODEs," to the journal, Examples and Counterexamples.

They studied a particular class of boundary value problems with periodic boundary conditions and proved that the solutions to such problems will retain their symmetry under certain conditions on the forcing terms. On the other hand, they also proved that there will exist solutions that will not retain symmetry under conditions on the derivative of the nonlinear term. This result generalizes the result given in Costa and Fang's paper for the breaking of symmetry.