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