Prolongation Structure Analysis of a Coupled Dispersionless System

We address the problem of integrability of a coupled dispersionless system recently introduced by Zhaqilao, Zhao and Li Chin. Phys. B 18 (2009) 1780 which physically describes the propagation of electromagnetic fields within an optical nonlinear medium, but also arrives in the physical description of a charged object dynamics in an external magnetic field. Following the prolongation structure analysis developed by Wahlquist and Estabrook, we derive a more general form of Lax pairs of the previous coupled dispersionless system and its concrete non-Abelian Lie algebra resorting to a hidden symmetry. Also, we construct the Bäcklund transformation of the system using the Riccati form of the linear eigenvalue problem.