A generalized Hirota-Satsuma coupled Korteweg-de Vries equation and Miura transformations

By introducing a 4 X 4 matrix spectral problem with three potentials, we propose a new hierarchy of nonlinear evolution equations. A typical equation in the hierarchy is a generalization of the Hirota-Satsuma coupled Korteweg-de Vries equation. Also, it is shown that the hierarchy possesses the generalized Hamiltonian form. Further, a Miura transformation related to the typical equation and its reductions are derived, from which some new coupled modified Korteweg-de Vries equations are obtained. (C) 1999 Elsevier Science B.V. All rights reserved.