Integrable models from PT-symmetric deformations

Details Integrable models from PT-symmetric deformations Integrable models from PT-symmetric deformations

2008-10-20

arxiv.org/abs/0810.3628v1

Journal of Physics A: Math. Theor. 42 (2009) 105206

Physics

Mathematical Physics

14 pages Latex

Scientific paper

10.1088/1751-8113/42/10/105206

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.

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