In this paper we propose a new model of the coherent pulsar radio emission, based on previous work of Ruderman and Sutherland (1975). We assume a non-stationary polar gap braking down via a number of localized spark discharges, feeding a corresponding subpulse-associated plasma columns in the pulsar magnetosphere. Central spark operates at the local pole of the surface magnetic field and other sparks perform more or less ordered circumferential motion around it due to the E×B drift. We argue that such an arrangement of the polar cap is supported by the observational data. We demonstrate that each spark occupies a region of the polar cap with a characteristic dimension approximately equal to the height of the gap. This is also a typical distance between sparks. The life time of each spark is very short (≤ 10μs) but they can reappear at approximately the same places due to heating of the surface beneath them by the back-streaming electrons. Thus, the sparks can operate at approximately the same place quite long, alternating between the developing and the terminating phase. The typical time span between two consecutive sparks is less than about 1 μs. We assume that the local surface magnetic field has a complicated multipolar structure with a radius of curvature of field lines smaller than the neutron star radius. Although this is not critical for our model, we further assume that the actual surface field has a sunspot like structure. If this is so, then charged particles accelerated within the high voltage gap region never leave the neutron star surface. This avoids the long standing "current closure" problem. However, the high energy curvature photons produced within the gap during the motion along closed field lines can reach the region above the gap, where the physical conditions are still suitable to produce clouds of secondary plasma due to the Sturrock's multiplication process. Each cloud has a broad energy distribution function. The Lorentz factor γ of a bulk plasma is about 100 but γ of the high energy tail is about few hundreds. The faster particles of the following plasma cloud can overcome the slower bulk particles of the preceding one, acting as a beam penetrating plasma. This ignites a typical beam-plasma instability generating well known electrostatic Langmuir waves. Detailed calculations show that the amplitude of these waves is high enough to cause a non-linear evolution, leading to soliton formation. The net charge of a relativistically moving soliton is a source of the coherent curvature radiation powerful enough to explain observed pulsar luminosities. It is worth emphasizing that, for the first time, this is a self-consistent model of pulsar radiation. The coherent curvature radio emission by solitons in our model is a consequence of a putative existence of a non-stationary polar gap braking down via exponentially developing sparks.