The paper “Traveling wave solution of the Kawahara equation joining distinct periodic waves“, co-authored by Pat Sprenger (Newton Institute, Cambridge), Tom Bridges, and Michael Shearer (North Carolina State University), has been published this week in the Journal of Nonlinear Science (link here). The paper combines jump conditions from the theory of conservation laws with dynamical systems theory of periodic orbits to find new travelling wave solutions which asymptote to distinct periodic solutions of the Kawahara equation. The image below is a screenshot of Figure 15 from the paper.