Miura Transformation between two Non-Linear Equations in 2+1 dimensions

Details Miura Transformation between two Non-Linear Equations in 2+1 dimensions Miura Transformation between two Non-Linear Equations in 2+1 dimensions

1998-03-06

arxiv.org/abs/solv-int/9803007v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, latex. Journal of Mathematical Physics (to appear)

Scientific paper

10.1063/1.532421

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 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.

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