On the equivalence between two perturbation techniques in fluid dynamics

The hydrodynamic equations governing the propagation of waves in one dimension are solved by successive approximations. Secular terms appear in a regular perturbation analysis, which limit the practical usefulness of such an approach. Two singular perturbation methods are described to remedy the presence of singularities. It is shown that the Poincaré-Linghthill-Kuo method and the method of characteristics are equivalent at least to first order in the amplitude of the perturbed velocity.