q- sl₂ and Associated Wave and Heat Equations

Abstract

For q ∈ (0, 1), the q-deformation of the sl 2 Lie algebra (denoted by q-sl 2 ) is introduced and we give its representation. The heat and wave equations associated to the genrators of the q-sl 2 are studied.

The Q‐Space Deformed Wave Equation

“…We recall some basic notations of the language of q-calculus (see [6][7][8][9]). e natural number n has the following q-deformation for q ∈ (0, 1):…”

The Q‐Time Deformed Wave Equation

“…(52) Note that, since the limit (when q ⟶ 0) of D q,t is D 0,t , the free-time wave equation is the limit case (when q ⟶ 0) of the q-time deformed wave equation (11).…”

Solution of Second Order Ordinary Differential Equation Associated with Toeplitz and Stiffness Matrices

“…By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes (Wazwaz, 2002;Altoum, 2018c;Gupta et al, 1995;Altoum, 2018b). In this study we consider the following equation:…”