Open AccessOrder reduction for critical traveling wave problems
Author(s) -
Elena Shchepakina
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1745/1/012106
Subject(s) - traveling wave , reduction (mathematics) , mathematical analysis , mathematics , reaction–diffusion system , projection (relational algebra) , model order reduction , order (exchange) , physics , geometry , algorithm , finance , economics
The paper deals with the order reduction for critical traveling wave problems. The specificity of such traveling waves is that they separate waves with qualitatively different behaviors. W e show how the application of the geometric theory of singular perturbations allows us to reduce the traveling wave problem for the original PDE system to the analysis the projection of the system onto its slow invariant manifold. W e illustrate this approach to the problem of finding the point-to-periodic traveling wave for the reaction-diffusion model.