Integrable models from PT-symmetric deformations
arXiv:0810.3628 · doi:10.1088/1751-8113/42/10/105206
Abstract
We address the question of whether integrable models allow for PT-symmetric deformations which preserve their intgrability. For this purpose we carry out the Painleve test for PT-symmetric deformations of Burgers and the Korteweg-De Vries equation. We find that the former equation allows for infinitely many deformations which pass the Painleve test. For a specific deformation we prove the convergence of the Painleve expansion and thus establish the Painleve property for these models, which are therefore thought to be integrable. The Korteweg-De Vries equation does not allow for deformations which pass the Painleve test in complete generality, but we are able to construct a defective Painleve expansion.
14 pages Latex
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