Verification and Invalidation of the Theory of Symplectic Manifold with Contact Degeneracies as Applied to the Classical Field Theory

Abstract

A theory of Symplectic Manifold with Contact Degeneracies (SMCD) was developed in [Zot'ev,2007]. The symplectic geometry employs an anti-symmetric tensor (closed differential form) such as a field tensor used in the classical field theory. The SMCD theory studies degeneracies of such form. In [Zot'ev,2011] the SMCD theory was applied to study a front of an electromagnetic pulsed field propagating into a region with no field. Here, the result of [Zot'ev,2011] is compared with the problem solution obtained using the well-known method presented in Whitham, G.B., Linear and nonlinear waves, 1974. It is shown that the SMCD theory prediction is not supported by the result obtained with the Whitham method.