Reciprocal link for 2 + 1-dimensional extensions of shallow water equations

Reciprocal transformations [1-3] are a useful tool in the study of integrable partial differential equations. Recently, there has been much interest in the equation of Fokas-Fuchssteiner-CamassaHolm (FFCH), originally derived by Fokas and Fuchssteiner [4] in the context of bi-Hamiltonian theory, and subsequently rederived as an equation for shallow water waves by Camassa and Holm [5]. The FFCH equation exhibits the weak Painlev~ property [6,7] and has a reciprocal link with the first negative flow of the KdV hierarchy [8,9]. In [10], the following nonisospectral 2+l-dimensional generalization of the FFCH equation was constructed: