Single and multi-vertices solitons in lattices of active Morse - van der Pol units

The dynamical evolution of one-dimensional lattice of active units (otherwise said particles) endowed with anharmonic Morse interactions and active-dissipative van der Pol negative friction is here studied both analytically and numerically. One of the directions of this evolution is the formation and stable propagation of dissipative soliton-like perturbations (in short solitons) against the background of some stationary displacement of units (pedestal). It is shown that the evolution of units at leading-front of the soliton is determined by mutual repulsive forces, while that of units at trailing-tail of the soliton is determined by the active-dissipative forces. Approximate analytically solvable models of the leading-front and the trailing-tail are obtained, which make it possible to predict soliton parameters and admissible range of pedestal values with high accuracy. There is also a scenario of N-vertices soliton formation emerging from a single soliton and (N-1)-vertices soliton. The possibility of controlling the number of vertices of multi-vertices solitons is offered, a feature which can be used in the problems of energy accumulation and transport in periodic structures. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The dynamical evolution of a one-dimensional lattice of active units with anharmonic Morse interactions and active-dissipative van der Pol negative friction is studied. The formation and stable propagation of dissipative soliton-like perturbations against a background stationary displacement of units are observed. Analytically solvable models of the leading-front and trailing-tail are obtained, which accurately predict soliton parameters and pedestal values. The formation of N-vertices solitons from a single soliton and (N-1)-vertices soliton is also observed, offering the possibility of controlling the number of vertices in multi-vertices solitons.