Modified Kortweg-de Vries equation approach to zero-energy states of graphene
1 Department of Physics, Tamkang University - Tamsui 25137, Taiwan
2 Physics & Applied Mathematics Unit, Indian Statistical Institute - Kolkata 700 108, India
Received: 31 August 2015
Accepted: 19 November 2015
We utilize the relation between soliton solutions of the modified Kortweg-de Vries (mKdV) and the combined mKdV-KdV equation and the Dirac equation to construct electrostatic fields which yield exact zero-energy states in graphene. The examples considered here are fairly general and it has also been shown that some of these examples reproduce the previously known results when parameters are chosen suitably.
PACS: 73.22.Pr – Electronic structure of graphene / 03.65.Pm – Relativistic wave equations / 47.35.Fg – Solitary waves
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