ALGEBRAIZATION OF BRIOSCHI-HALPHEN EQUATION

U.N. Bassey, U.S. Idiong

Abstract


The Brioschi-Halphen Equation (BHE) is a second order differential equation in the complex domain obtained by a two-step variable transformation of the Lam\'e equation in the Weierstrass form. In this paper, we present a new algebraization of the BHE by writing its operator as an element of the universal enveloping algebra of the Lie algebra $\mathfrak{s}\ell(2,\mathbb{C}).$ We also obtain a Lie algebraic potential from Lie algebraic equation so formed by using a suitable guage transformation. A polynomial solution of the Lie algebraic equation obtained is presented.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

IJDEA, Academic Publications, Ltd.