One-Way Wave Operator

The second-order partial differential wave Equation (Cauchy’s first equation of motion), derived from Newton’s force equilibrium, describes a standing field consisting two waves propagating in opposite directions, and is, therefore, “two-way equation”. Due to the second order differentials analytical solutions only exist few cases. “binomial factorization” linear two-way operator into first-order one-way operatoras has been known for decades used geophysics. When binomial factorization approach is applied spatial operator, this results complex mathematical terms containing so-called “Dirac operator” which particular exist. In 2014, hypothetical “impulse flow equilibrium” led “one-way equation” which, due its differentials, can be more easily solved than equation. To date conversion operators unsolved. By considering vector velocity, “synthesis” leads “general one-way/two-way equivalence”. For constant velocity equivalence with d’Alembert achieved. findings are transferred commonly mechanical electromagnetic types. theory offer new opportunities science engineering advanced calculations.