Duality methods for a class of quasilinear systems

TL;DR

This paper explores duality methods to solve nonlinear Hodge systems, establish boundary value problem well-posedness, and uncover symmetries through Hodge-Bäcklund transformations, advancing understanding of quasilinear systems.

Contribution

It introduces duality techniques for explicit solutions, analyzes well-posedness, and reveals symmetries in quasilinear systems using Hodge-Bäcklund transformations.

Findings

Explicit solutions to nonlinear Hodge systems

Proof of boundary value problem well-posedness

Identification of symmetries via Hodge-Bäcklund transformations

Abstract

Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially different forms of the equations.