Abstract
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 hierarchy, which are reduced further into integrable ordinary differential equations in the invariant set produced by the stationary Kaup–Newell equation. The Abel–Jacobi coordinates are introduced to straighten out the flows, from which quasi-periodic solutions of the 2+1 dimensional modified Korteweg–de Vries equation are obtained in terms of the Riemann theta functions.
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