Ehrenfest theorem for nonlinear Klein-Gordon solitary waves

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Abstract
A theorem which describes the Newtonian dynamics of the center of mass (as defined with respect to the energy density) of nonlinear Klein-Gordon-type solitary waves is proved. It appears as a generalization of Ehrenfest’s theorem in quantum mechanics, which describes the Newtonian dynamics of the center of mass (as defined with respect to the probability density) of the linear wave functions. As an example, the interaction of recently discovered two-dimensional pulsons [cf. E. M. Maslov, Phys. Lett. A 151, 47 (1990)] is considered.