This research investigates the motion of a particle in a highly ionized plasma using the particle-in-cell (PIC) method, a classical approach to solving the Vlasov-Maxwell or Vlasov-Poisson equations. The PIC technique combines a particle-based solution of the Vlasov equation with a grid-based solution for the field equations. In this method, the plasma distribution is represented by macroparticles that approximate the initial particle distribution and evolve over time as their equations of motion are numerically integrated under self-consistent electromagnetic fields. We focus on the simulation of electrostatic solitary waves (ESWs) also known as isolated electrostatic structures (IESs), solitary bipolar pulses, or solitary electrostatic structures (ESSs) which have been detected in space plasmas since 1982. In satellite data, ESWs appear as isolated, nonlinear sinusoidal structures, such as unipolar, bipolar, or tripolar electric field pulses. These distinctive characteristics make ESWs a rich subject for study in nonlinear plasma dynamics. We perform one-dimensional electrostatic simulations of a system comprising two electron beams and one ion beam propagating along a uniform magnetic field. The simulation parameters, such as density ratios and thermal velocities of electron and ion components, are adjusted to trigger and study development of plasma instabilities causing ESWs.