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Kinetic and hydrodynamic travelling wave solutions of 2-velocity models of the extended Boltzmann equation

Abstract We find new types of travelling wave solutions which join rest points of general 2- velocity models of the extended Boltzmann equation. The new solutions exhibit oscillations of the density around a stationary state. For the first time we derive the hydrodynamic approximations for such models. We study the travelling wave solutions of these equations as well, and compare them with the corresponding solutions of the kinetic equations.