2006/10/31 by G. Dattoli, Dattoli, G., D. Levi +1
Engineering · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Scientific Research and Discoveries #Sports Dynamics and Biomechanics #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0610076
arxiv created 2006/10/31 · openalex publication_date 2006/10/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the umbral correspondence between differential equations can be achieved by means of a suitable transformation preserving the algebraic structure of the problems. We present the general properties of these transformations, derive explicit examples and discuss them in the case of the Appèl and Sheffer polynomial families. We apply these transformations to non-linear equations, and discuss how the relevant solutions should be interpreted.