2024/04/28 by L. V. Bogdanov, Bogdanov, L. V.
Mathematics · Physics and Astronomy · #35Q75 #37K10 #37K15 #37K25 #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2404.18078
openalex publication_date 2024/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these equations can be interpreted in terms of Abelian gauge fields on the geometric background defined by the dispersionless system. They are also connected with the linearisation of initial systems. We construct solutions to these linear equations in terms of wave functions of the Lax pair for dispersionless system, which is represented in terms of some vector fields.