Miura transformation between two non-linear equations in 2+1 dimensions

A Dispersive Wave equation in 2 + 1 dimensions (2LDW) widely discussed by different authors is shown to be nothing bur the modified version of the Generalized Dispersive Wave equation (GLDW). Using Singularity Analysis and techniques based upon the Painleve Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW equation into the GLDW equation. Through this Miura transformation we shall also present the Lax pair of the 2LDW equation as well as some interesting reductions to several already known integrable systems in 1 + 1 dimensions. As the 2LDW equation arises from a Miura transformation we propose that it should be treated conventionally as a Modified Equation. In this case, we propose its designation as The MGLDW Equation. (C) 1998 American Institute of Physics.