A note on the Painlevé analysis of a (2 + 1) dimensional Camassa–Holm equation

We investigate the Painlevé analysis for a (2 + 1) dimensional Camassa–Holm equation. Our results show that it admits only weak Painlevé expansions. This then confirms the limitations of the Painlevé test as a test for complete integrability when applied to non-semilinear partial differential equations.