Binary Bell polynomials, Hirota bilinear approach to Levi equation

Combining the binary Bell polynomials and Hirota method, we obtained two kinds of equivalent bilinear equations for the Levi equation. Then, we got the double Wronskian solutions of the Levi equation by virtue of one of the bilinear equations. Furthermore, we constructed the bilinear Bäcklund transformation and the Lax pair. Finally, we also derived the Darboux transformation and the infinite conservation laws of the Levi equation.