Ambartsumian's celebrated hypothesis that stellar flares and other phenomena of stellar instability are due to a novel source of energy and a novel means of transporting this energy to the outer layers of the star has drawn the attention of electrodynamicists to a number of fundamental problems. One of these problems, namely the energy transport problem, is the subject of this communication. Herein, by assuming that the matter of the star is an isotropic collisionless plasma, from Maxwell's field equations and Newton's equation of motion with nonlinear Lorentz driving force, we have derived a vector differential equation for electromagnetic wave propagation. This equation contains the Debye radius and the plasma frequency as parameters, and reduces to the well-known wave equation when its nonlinear terms are neglected. We have indicated that the nonlinear equation has cohesive (solitary) wave solutions for both the longitudinal and transverse components of the electromagnetic field. Such cohesive waves are appropriate for transporting energy from the prestellar core of the star to its outer layers since they hold their shape, are free from dispersive distortion, and can carry energy in discrete amounts.