Zulfia Ziwave Equation (ZZE): Wave Generation on Certified Domains under ZBPT Framework

Abstract

The classical wave equation assumes wave existence over the entire samplespace Ω. In this paper, we introduce the Zulfia Ziwave Equation (ZZE) basedon Zulfia Bi-Face Probability Theory (ZBPT). In ZBPT, probability is notassumed on full sample spaces but is generated only on certified domains Dc.The central governing equation is:∂2ΨZi∂t2 = c2 C(Dc) ∇2ΨZiConsequently, a Ziwave ΨZi exists if and only if its domain is certified(C(Dc) = 1). We derive the governing equation, prove its boundedness bycertified measure μ(Dc), and establish its distinction from the classical waveequation.