From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

TL;DR

This paper proves the non-existence of smooth solutions for a complex quasi-linear system in nonlinear elasticity and explores its connection to polynomial integrals in Hamiltonian systems.

Contribution

It introduces a novel analysis of a mixed elliptic-hyperbolic system in nonlinear elasticity and links it to polynomial integrals in classical Hamiltonian dynamics.

Findings

No smooth solutions exist for the proposed system.

The system is of mixed elliptic-hyperbolic type.

A relation between the elasticity model and Hamiltonian polynomial integrals is established.

Abstract

We prove non existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Nonlinear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.