Solitary Waves in the Morse–Van Der Pol Chain with Nonlocal Particle Interactions

Abstract

Using numerical simulation methods, we find that in the generalized Morse–van der Pol model for a chain of active particles with account of their nonlocal interactions, the emergence and stable propagation of dissipative kinks and solitons are possible. Switching from local to nonlocal interactions results in a decrease in the maximum particle velocities and an increase in the general width of both the kink and the soliton. It is shown that the approximate analytical model describing the leading front of the solitary wave based on two-particle collisions loses its relevance in the generalized chain model. We propose an efficient numerical procedure for determining the shape of the traveling wave in a conservative Morse chain with nonlocal interactions; the procedure is based on solving an advanced-delay differential equation.