Two-dimensional simulations, both Vlasov and particle-in-cell, are presented that show the evolution of the field and electron distribution of finite-width, nonlinear electron plasma waves. The intrinsically intertwined effects of self-focusing and dissipation of field energy caused by electron trapping are studied in simulated systems that are hundreds of wavelengths long in the transverse direction but only one wavelength long and periodic in the propagation direction. From various initial wave states, both the width at focus Delta(m) relative to the initial width Delta(0) and the maximum field amplitude at focus are shown to be a function of the growth rate of the transverse modulational instability gamma(TPMI) divided by the loss rate of field energy nu(E) to electrons escaping the trapping region. With dissipation included, an amplitude threshold for self-focusing gamma(TPMI)/nu(E)similar to 1 is found that supports the analysis of Rose [Phys. Plasmas 12, 012318 (2005)].