Hermite-Halphen-Bloch solution of two-gap Lam\'e equation
Jun-ichiro Kishine, A. S. Ovchinnikov
TL;DR
This paper constructs explicit solutions for the two-gap Lamé equation using Hermite-Halphen-Bloch methods and provides formulas to determine the energy band structure.
Contribution
It introduces a novel Hermite-Halphen-Bloch approach for solving the two-gap Lamé equation and derives closed-form expressions for energy dispersion relations.
Findings
Explicit Hermite-Halphen-Bloch solutions for two-gap Lamé equation
Closed-form formulas for energy band dispersion
Advances understanding of spectral properties of Lamé operators
Abstract
We construct the Hermite--Halphen--Bloch solution for the two-gap () Lam\'e equation of Jacobian form and give closed formulae to calculate the energy band dispersion relation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Fractional Differential Equations Solutions