Backlund Transformations for Darboux Integrable Differential Systems:\n Examples and Applications

2014/07/10 by Ian Anderson, Mark E. Fels, Anderson, Ian M. +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #34A26 #37K35 #58A15 #58J70 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1407.3011

openalex publication_date 2014/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the article arXiv:1108.5443 we established a general group-theoretical\napproach to the construction of B "acklund transformations. We then showed how\nthis construction can be applied to construct B "acklund transformation between\nequations which are Darboux integrable. Here we give a number of detailed\nexamples and new applications which demonstrate the theory. In particular our\nfinal example demonstrates how our group theoretical approach produces all the\nB "acklund transformations in arXiv:0707.4408. We also prove, using group\nmethods, a non-existence theorem for B "acklund transformatons which disagrees\nwith part 2 of Theorem 1 in arXiv:0707.4408.\n

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