A Physical Approach to Polya's Conjecture

TL;DR

This paper proposes a novel physical perspective on Polya's conjecture by exploring a duality between wave and soliton solutions on a surface, specifically focusing on the disc case.

Contribution

It introduces a duality framework linking wave and soliton solutions to approach Polya's conjecture from a physical standpoint.

Findings

Identifies a potential duality between waves and solitons on surfaces.

Focuses on the special case of the disc to illustrate the approach.

Suggests a new direction for analyzing Polya's conjecture through physical models.

Abstract

The similarity between the Polya's conjecture and the Bonomol'nyi bound remind us to consider a physical approach to Polya's conjecture. We conjecture a duality between the waves and the soliton solutions on the surface. We consider the special case in the disc.