Bäcklund transformation and soliton solutions for the coupled dispersionless equations

The Painlevé test is employed to predict the integrability properties of the coupled dispersionless system equations. From the analysis, it is shown that these systems admit the Painlevé property and possess Hirota bilinear form. The one-soliton solutions of the coupled dispersionless system are generated through Bäcklund transformation using the linear eigenvalue problem.