In this study, the transonic gas equation will be considered. For q∈(0,1), q-deformation of transonic gas equation (q-transonic) are studied, we use q-derivative (or Jackson derivative) to solve transonic gas equation.
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.
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