Self-focusing of high power, short laser pulses is considered for the purpose of identifying physical parameters that allow a remotely controllable ionization in the atmosphere. The propagation equation including diffraction, group velocity dispersion, Kerr nonlinearity and bound electrons effects is derived. A Lagrange density describing the propagation equation depending on a general pulse amplitude is presented for a propagation regime in the absence of ionization and plasma defocusing. Lagrange equations for beam parameters are determined and solved for a particular ansatz describing a chirped Gaussian beam with a curvature function. It is demonstrated that nonlinear effects not only cause transverse focusing but also temporally enhance the group velocity dispersion. A mutual interrelation between the pulse power, curvature, and chirp parameters is derived explicitly. Moreover, the location where the pulse self-focuses is addressed within the limits on the propagation distance along which the beam shape and the initial symmetry are preserved. Thus, a complete analytical structure of remote ionization is underlined. (C) 2008 American Institute of Physics.