DBAR problem

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The DBAR problem is the problem of solving the differential equation

for the function , where is assumed to be known and is a complex number in a domain . The operator is called the DBAR operator

The DBAR operator is nothing other than the complex conjugate of the operator

denoting the usual differentiation in the complex -plane.

The DBAR problem is of key importance in the theory of integrable systems[1] and generalizes the Riemann–Hilbert problem.


  1. ^ Konopelchenko, B. G. "On dbar-problem and integrable equations". arXiv:nlin/0002049Freely accessible.