2025/10/10 by Łukasz Chomienia, Chomienia, Łukasz, A. M. Grundland +1
Engineering · Mathematics · Physics and Astronomy · #17B80 #35A30 #35Q31 #53A05 #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2510.09576
openalex publication_date 2025/10/10 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/30
The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the introduction of the notion of quasi-rectifiability of vector fields and its application to both elastic and non-elastic wave superpositions. It is shown that the smallest real Lie algebra containing vector fields associated with the waves admitted by the Euler system is isomorphic to an infinite-dimensional Lie algebra which is the semi-direct sum of an Abelian ideal and the three-dimensional real Lie algebra. The maximal Lie module corresponding to the Euler system can be transformed, by an angle preserving transformation, to this algebra which is quasi-rectifiable and describes the behavior of wave superpositions. Based on these facts, we are able to find a parametrization of the region of non-elastic wave superpositions which allows for the construction of the reduced form of the Euler system.