Nonlinear Periodic Waves in a Deformable Medium Modeled by Chains of Active Morse–van der Pol Particles

Abstract— The generation and propagation of nonlinear periodic waves in a deformable medium modeled by different chains of active Morse–van der Pol particles are studied by numerical modeling methods. The intervals of change in wave periods are determined within a broad range of chain lengths. It is shown that, in short chains, conservative Morse forces are much greater than spatially dependence active friction forces and, as a consequence, the wave process occurs according to a conservative scenario. In long chains, the transformation of a nonlinear periodic wave into a dissipative soliton with a minimum velocity corresponding to a maximum period value has been revealed. It has been established that the dependence of the minimum period on the number of particles in a chain is almost linear. Instability in the propagation of initial perturbations composed of several previously identified identical periodic solutions is demonstrated.