Miura Transformation between two Non - Linear Equations in 2 + 1 dimensions
نویسندگان
چکیده
A Dispersive Wave Equation in 2 + 1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painlevé 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 sytems 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 1 Miura trans. for two equations in 2 + 1 2
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