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DBAR problem

From Wikipedia, the free encyclopedia

The DBAR problem, or the -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:[1]

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, Schrödinger operators and generalizes the Riemann–Hilbert problem.[1][2][3]

Citations

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References

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  • Ablowitz, Mark J.; Fokas, A. S. (2003). Complex Variables: Introduction and Applications. Cambridge University Press. pp. 516, 598–626. ISBN 978-0-521-53429-1.
  • Konopelchenko, B. G. (2000). "On dbar-problem and integrable equations". arXiv:nlin/0002049.