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 ∂r...

In tomography it has been recognized that the finiteness of the frequency content of seismic data leads to interference effects in the process of medium reconstruction, that need to be accounted for. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here, we consider single-scattered body waves and develop from our earlier work ...

T he foundation of seismology is the theory of wave motion, a complicated concept that is still after centuries of experiments and speculations by many of the very greatest scientists an area of active research in many disciplines. Even simple forms of wave motion are difficult to describe verbally; but, ironically, the simplest type of wave is remarkably easy to describe (and subsequently anal...

We consider a cubic nonlinear wave equation with highly oscillating cubic coefficient and wave packet initial data. Using a regularization step of the initial data, we give a low regularity justification of the Nonlinear Schrödinger equation as the envelope equation.

Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation. Further study of multiparticle systems has us looking into the mathematics of tensor products of Hilbert spaces. The principles of linearity and superpositi...

Physical wavelets are localized solutions of the scalar wave equation or Maxwell’s equations, obtained by extending fundamental solutions to complex space-time in the sense of hyperfunctions. The imaginary space-time variables y, which must form a time-like vector, act as scale parameters generalizing the scale variable of wavelets in one dimension. They determine the shape of the wavelets in s...