A global algorithm for the computation of traveling dissipative solitons

An algorithm is proposed to calculate traveling dissipative solitons for the FitzHugh-Nagumo equations. It is based on the application of the steepest descent method to a certain functional. This approach can be used to find solitons whenever the problem has a variational structure. Since the method...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Authors: Yung-Sze Choi, Connors, Jeffrey M
Format: Article
Language:English
Subjects:
Algorithms
Bifurcations
Configuration management
Domains
Energy dissipation
Physical properties
Solitary waves
Steepest descent method
Online Access:Get full text
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Summary:An algorithm is proposed to calculate traveling dissipative solitons for the FitzHugh-Nagumo equations. It is based on the application of the steepest descent method to a certain functional. This approach can be used to find solitons whenever the problem has a variational structure. Since the method seeks the lowest energy configuration, it has robust performance qualities. It is global in nature, so that initial guesses for both the pulse profile and the wave speed can be quite different from the correct solution. Also, bifurcations have a minimal effect on the performance. With an appropriate set of physical parameters in two dimensional domains, we observe the co-existence of single-soliton and 2-soliton solutions together with additional unstable traveling pulses. The algorithm automatically calculates these various pulses as the energy minimizers at different wave speeds. In addition to finding individual solutions, this approach could be used to augment or initiate continuation algorithms.
ISSN:2331-8422