Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIB. Non-Subgroup Basis

2025/06/07 by G. S. Pogosyan, Pogosyan, G. S., Alexander Yakhno +1
Mathematics · Engineering · #Mathematics and Applications #Differential Equations and Boundary Problems #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2506.06827

Abstract

The paper describes solutions of the Laplace-Beltrami equation on two-dimensional two-sheeted hyperboloid for three non-subgroup coordinate systems: semi-sircular parabolic, elliptic parabolic and hyperbolic parabolic. The coefficients of interbasis expansions of solutions in the specified coordinate systems through some subgroup bases are calculated. A contraction procedure for all normalized eigenfunctions in three non-subgroup coordinate systems from the hyperboloid to the Euclidean plane is realized.

Citations

• Reviewing the Helmholtz Equation on Euclidean Plane and Interbasis Expansions
• On the factorization method in quantum mechanics

Related

• Lie Algebra Contractions and Interbasis Expansions on Two-Dimensional Hyperboloid IIA. Subgroup Basis
• Lie Algebra Contractions and Separation of Variables on Two-Dimensional Hyperboloids. Coordinate Systems
• A description of several coordinate systems for hyperbolic spaces
• Beltrami's theorem via parabolic geometry
• On factorization and solution of multidimensional linear partial differential equations