A connection between HH3 and Korteweg–de Vries with one source

Abstract

In the system made of Korteweg–de Vries with one source, we first show by applying the Painlevé test that the two components of the source must have the same potential. We then explain the natural introduction of an additional term in the potential of the source equations while preserving the existence of a Lax pair. This allows us to prove the identity between the traveling-wave reduction and one of the three integrable cases of the cubic Hénon–Heiles Hamiltonian system.