The two-dimensional second-order differential spectral problem: compatibility conditions, general BTs and integrable equations
- 1 February 1988
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 4 (1) , 151-163
- https://doi.org/10.1088/0266-5611/4/1/013
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.Keywords
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