Integrability of the coupled KdV equations derived from two-layer fluids: Prolongation structures and Miura transformations

Abstract The Lax integrability of the coupled KdV equations derived from two-layer fluids [S.Y. Lou, B. Tong, H.C. Hu, X.Y. Tang, Coupled KdV equations derived from two-layer fluids, J. Phys. A: Math. Gen. 39 (2006) 513–527] is investigated by means of prolongation technique. As a result, the Lax pairs of some Painleve integrable coupled KdV equations and several new coupled KdV equations are obtained. Finally, the Miura transformations and some coupled modified KdV equations associated with the Lax integrable coupled KdV equations are derived by an easy way.

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