Spherical One-Way Wave Equation

The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it necessary to achieve consistency between gradient, divergence and Laplace operators establish, beside the conventional radial Nabla operator ∂Φ/∂r, a new variant ∂rΦ/r∂r. two variants differ near field term Φ/r whereas far r≫0 there asymptotic approximation. Surprisingly, more complicated gradient ∂rΦ/r∂r results unexpected simplifications for – only waves with 1/r amplitude decrease. Thus calculation always remains elementary without wattless imaginary fields, Bessel functions are obsolete.