Ernie Kalnins, George S. Pogosyan, Alexander Yakhno, “Separation of Variables and Contractions on Two-Dimensional Hyperboloid”, SIGMA, 2012, Volume 8,105, 11 pp.

This article is cited in 1 paper

Separation of Variables and Contractions on Two-Dimensional Hyperboloid

Ernie Kalnins^a, George S. Pogosyan^bc, Alexander Yakhno^c

^a Department of Mathematics, University of Waikato, Hamilton, New Zealand
^b International Center for Advanced Studies, Yerevan State University, A. Manougian 1, Yerevan, 0025, Armenia
^c Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, Jalisco, Mexico

Abstract: In this paper analytic contractions have been established in the $R\to\infty$ contraction limit for exactly solvable basis functions of the Helmholtz equation on the two-dimensional two-sheeted hyperboloid. As a consequence we present some new asymptotic formulae.

Keywords: analytic contraction; separation of variables; Lie group; Helmholtz equation.

MSC: 70H06; 35J05

Received: August 9, 2012; in final form December 19, 2012; Published online December 26, 2012

Language: English

DOI: 10.3842/SIGMA.2012.105