**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. These equations when set in the electromagnetic domain are a novel mathematical reformulation of the Maxwell equations: $\mathscr{M}(\vb u,\vb B,\vb E) = \big\{\vb E= \vb u \cross \vb B;\,$ $\vb u= (\vb B \cross \vb E)/\norm{\vb B}^2;\,$ $\vb B = (\vb E \cross \vb u)/\norm{\vb u}^2 \big\}$ where $\vb u$ is a velocity vector. Furthermore, the expressions for the permittivity $\epsilon_0$, permeability $\mu_0$ and the magnetic flux density $\vb B$ are obtained by manipulating $\mathscr{M}.$ As an application of $\mathscr{M}$ 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.

**Key Words: **

Wave equation, Maxwell equations, EM-waves, EM-soliton, Ball lightning, Bimodal waves

**Posted in: ** Bimodal Waves in Vacuum

**Article Reference: **787

**Article Status:** Published in Proceedings

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