Quasilinear systems with linearizable characteristic webs

TL;DR

This paper classifies a special class of quasilinear systems in Riemann invariants where the characteristic webs are linearizable on all solutions, showing they can be transformed into uncoupled Hopf equations.

Contribution

It provides a complete classification of such systems and demonstrates their transformation into simpler equations via reciprocal transformations.

Findings

Characteristic webs are linearizable on all solutions under simple second-order constraints.

Systems with more than three components can be transformed into uncoupled Hopf equations.

The classification is local, applicable in a neighborhood of solutions.

Abstract

We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic webs on all solutions imposes simple second-order constraints for the characteristic speeds of the system. It is demonstrated that every such system with n>3 components can be transformed by a reciprocal transformation to n uncoupled Hopf equations. All our considerations are local.