Abstract
Nonlinear evolution systems in two spatial dimensions integrable by the spectral problem ( delta x2- sigma 2 delta y2+ phi 1 delta x+ phi 2 delta y+U(x, y)) psi =0 are considered. It is shown that such systems possess the matrix commutativity representation (T1M,T2M)=0 which is equivalent to the usual 'L-A-B triad' representation of the compatibility condition. General Backlund transformations (BTS) and the general form of integrable equations are found by the recursion operator method.
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