2008/10/20 by Paulo E G Assis, Paulo E. G. Assis, Andreas Fring · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/42/10/105206
published as Journal of Physics A: Math. Theor. 42 (2009) 105206 · 14 pages Latex
arxiv created 2008/10/20 · openalex publication_date 2009/02/17 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/30
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.