Quasi-periodic solutions of the 2+1 dimensional modified Korteweg-de Vriesequation

A new 2 + 1 dimensional modified Korteweg-de Vries equation is proposed and decomposed into the first two members in the well-known Kaup-Newell hierar chy, which are reduced further into integrable ordinary differential equati ons in the invariant set produced by the stationary Kaup-Newell equation, T he Abel-Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the 2 fl dimensional modified Korteweg-d e Vries equation are obtained in terms of the Riemann theta functions. (C) 1999 Published by Elsevier Science B.V. All rights reserved.