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Integrable models from PT-symmetric deformations

Assis, P. E. G. and Fring, A. (2009). Integrable models from PT-symmetric deformations. Journal of Physics A: Mathematical and Theoretical, 42(10), doi: 10.1088/1751-8113/42/10/105206

Abstract

We address the question of whether integrable models allow for -symmetric deformations which preserve their integrability. For this purpose we carry out the Painlevé test for -symmetric deformations of Burgers and the Korteweg–De Vries equations. We find that the former equation allows for infinitely many deformations which pass the Painlevé test. For a specific deformation we prove the convergence of the Painlevé expansion and thus establish the Painlevé property for these models, which are therefore thought to be integrable. The Korteweg–De Vries equation does not allow for deformations which pass the Painlevé test in complete generality, but we are able to construct a defective Painlevé expansion.

Publication Type: Article
Publisher Keywords: PARTIAL-DIFFERENTIAL-EQUATIONS, NON-HERMITIAN HAMILTONIANS, DE-VRIES EQUATION, 2D SU(N) YM, PAINLEVE PROPERTY, CALOGERO MODEL, BURGERS-EQUATION, CONVERGENCE, EXPANSIONS, SYSTEMS
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/773
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