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- W1858381411 abstract "The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, underdamped, over-damped and the critical one. It is shown that in all three cases solution is oscillating in time but is unbounded and non-periodic. By q-periodic function modulation, the self-similar microstructure of the solution for small time intervals is derived. In the critical case with degenerate roots, the second linearly independent solution is obtained as a limiting case of two infinitesimally close roots. It appears as standard derivative of q-exponential and is rewritten in terms of the q-logarithmic function. We extend our result by constructing n linearly independent set of solutions to a generic constant coefficient q-difference equation degree N with n degenerate roots." @default.
- W1858381411 created "2016-06-24" @default.
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- W1858381411 date "2011-07-13" @default.
- W1858381411 modified "2023-09-27" @default.
- W1858381411 title "Q-Damped Oscillator and Degenerate Roots of Constant Coefficients q-Difference ODE" @default.
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