Scheduled Saturday Dec 17, 2022 7:00 PM (GMT) London, 11:00 AM California, 2:00 PM New York, 10:00 PM Moscow

Abstract Waves of all types are described mathematically using partial differential equations. Here, departing from this tradition, I describe waves using a novel system of three simultaneous vector algebraic equations: $\mathscr{M}(\vb u,\vb a,\vb r) = \big\{\vb r= \vb u \cross \vb a;\,$ $\vb u= (\vb a \cross \vb r)/\norm{\vb a}^2;\,$ $\vb a = (\vb r \cross \vb u)/\norm{\vb u}^2 \big\}$ which define Maxwellian wave dynamics for any fields $\vb a$ and $\vb b$ that support wave action and $\vb u$ a velocity vector. That is $\mathscr{M}(\vb u,\vb B,\vb E)$ is a novel reformulation of the Maxwell equations in vacuum. Furthermore, the expressions for the permittivity $\epsilon_0$, permeability $\mu_0$ and the magnetic flux density $\vb B$, in terms of action $h$, elementary charge $e$ and speed of light $c$, are obtained by manipulating $\mathscr{M}$ with the assumption that an EM-wave has action and transports charge. As an application of $\mathscr{M}(\vb u,\vb B,\vb E)$ I show that three dimensional spherical EM-wave structures do exist, in theory at least. They are stationary with finite dimensionality and could provide the basis for describing EM-solitons, which in turn could be used to describe many natural phenomena, including ball lightning among others. Instead of working with fields I reformulate $\mathscr{M}$ in terms of flux vectors $\vb A$ and $\vb R$. Using $\mathscr{M}(\vb u, \vb A, \vb R)$ I describe rotary waves (propeller-like instead of ripples on a pond) and show that rotary waves could be the basis to describe particles, physically, as solitons in terms of Maxwellian wave dynamics.

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