Searcharxiv⌕ Search

arXiv subjects

Natale Manganaro

Publications and source records attributed to Natale Manganaro.

4 recordsLinked to original sources
arXiv2025

Differential constraints for hyperbolic systems through k-Riemann invariants

In this paper we develop a reduction procedure for determining exact wave solutions of first order quasilinear hyperbolic one-dimensional nonhomogeneous systems. The approach is formulated within the theoretical framework of the method of differential constraints and it makes use of the $k-$Riemann invariants. The solutions obtained permit to characterize rarefaction waves also for nonhomogeneous models so that Riemann problems can be solved. Applications to the Euler system describing an ideal fluid with a source term are given.

math-ph↗
arXiv2024

A reduction procedure for determining exact solutions of second order hyperbolic equations

In this paper we develop a systematic reduction procedure for determining intermediate integrals of second order hyperbolic equations so that exact solutions of the second order PDEs under interest can be obtained by solving first order PDEs. We give some conditions in order that such a procedure holds and, in particular, we characterize classes of linear second order hyperbolic equations for which the general solution can be found.

math-ph↗
arXiv2023

Solutions to the wave equation for commuting flows of dispersionless PDEs

Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction procedure of differential constraints to obtain a complete set of solutions of such an equation for some fixed velocities a^2(u,v). As a result, we present some examples of Hamiltonian integrable systems (as the shallow water equations) with relative symmetries, conserved quantities and solutions.

math-ph↗