Finite Mechanical Proxies for a Class of Reducible Continuum Systems

TL;DR

This paper introduces a method to exactly reduce certain nonlinear wave equations to finite spring-mass systems, providing a physically interpretable proxy for complex continuum models.

Contribution

It establishes a novel exact finite reduction technique linking spectral descriptions of nonlinear wave equations to discrete mechanical models.

Findings

Finite reduction yields a physically meaningful spring-mass system

Inverse eigenvalue problem solution connects spectral and mechanical models

Provides a new approach for analyzing nonlinear wave equations

Abstract

We present the exact finite reduction of a class of nonlinearly perturbed wave equations, based on the Amann-Conley-Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral finite description derived from A-C-Z and a discrete mechanical model, a well definite finite spring-mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.