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Weakly nonlinear ion sound waves in gravitational systems

Ion sound waves are studied in a plasma subject to gravitational field. Such systems are interesting by exhibiting a wave growth that is a result of energy flux conservation in inhomogeneous systems. The increasing wave amplitude gives rise to an enhanced interaction between waves and plasma particles that can be modeled by a modified Korteweg-de Vries equation. Analytical results are compared with numerical Particle-in-Cell simulations of the problem. Our code assumes isothermally Boltzmann distributed electrons while the ion component is treated as a collection of individual particles interacting through collective electric fields. Deviations from quasi neutrality are allowed for.