Work

The generalised hodograph method for non-diagonalisable integrable systems of hydrodynamic type

Year: 2026

Type: article

Abstract: We extend the generalised hodograph method to non-diagonalisable integrable systems of hydrodynamic type coming from F-manifolds. The method allows the construction of solutions starting from the symmetries of the system. In the diagonal case, the completeness of the symmetries follows from the integrability conditions that ensure the applicability of a Darboux’s theorem on Pfaffian systems. In the regular non-diagonalisable case the validity of this theorem relies on some further assumptions that we discuss in detail. Under these assumptions, the method provides the general solution as in Tsarev’s diagonal case.

Source: Nonlinearity

DOI: 10.1088/1361-6544/ae65fd

Authors: Paolo Lorenzoni, Sara Perletti, Karoline van Gemst

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca, University of Milano-Bicocca

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Istituto Nazionale di Fisica Nucleare, Ministero dell'Università e della Ricerca, Gruppo Nazionale per la Fisica Matematica