Singularity structure analysis and Hirotaʹs bilinearisation of the coupled integrable dispersionless equations

We investigate the singularity structure analysis of coupled integrable dispersionless equations and we show that the system possesses the Painlevé property. The associated Bäcklund transformation is constructed and Hirotaʹs bilinearisation is also obtained through dependent variable transformations. Finally, we reduce the system to the well-known sine-Gordon equation.