Integrable models from PT-symmetric deformations

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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Cited by in corpus (6)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• PT-symmetric deformations of integrable models
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Time-delay and reality conditions for complex solitons
• From real fields to complex Calogero particles
• Complex BPS solitons with real energies from duality