mKdV equation approach to zero energy states of graphene

TL;DR

This paper uses soliton solutions of the mKdV and related equations to design electrostatic fields that produce exact zero energy states in graphene, linking nonlinear wave equations with quantum states.

Contribution

It introduces a novel method to generate zero energy states in graphene using soliton solutions from the mKdV equation, bridging nonlinear dynamics and quantum material engineering.

Findings

Exact zero energy states in graphene can be engineered using soliton solutions.

The approach connects nonlinear wave equations with quantum states in 2D materials.

Electrostatic fields based on soliton solutions produce predictable zero energy states.

Abstract

We utilize the relation between soliton solutions of the mKdV and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero energy states of graphene.