1998/12/04 by Robert Conte, R. Conte, Conte, R.
Physics and Astronomy · #Black Holes and Theoretical Physics #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI #solv-int
paper · pdf · doi:10.48550/arxiv.solv-int/9812008
16 pages, no figure, standard Latex, to appear in the proceedings of ``Nonlinear dynamics: integrability and chaos'', Tiruchirapalli, 12--16 Feb 1998, ed. S. Daniel
arxiv created 1998/12/04 · openalex publication_date 1998/12/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The ``truncation procedure'' initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Bäcklund transformation follows by an elimination, thus proving the integrability. We present the state of the art of this powerful technique. The easy situations were all handled by the WTC one-family truncation and its homographically invariant version. An updated version of this method has been recently developed, which is now able to handle the Kaup-Kupershmidt and Tzitzéica equations. It incorporates a new feature, namely the distinction between two entire functions usually mingled, which are shown to be linked by formulae established by Gambier for his classification.