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Persistence of travelling waves in a generalized Fisher equation
journal contribution
posted on 2023-06-08, 07:56 authored by Yuliya KyrychkoYuliya Kyrychko, Konstantin BlyussKonstantin BlyussTravelling waves of the Fisher equation with arbitrary power of nonlinearity are studied in the presence of long-range diffusion. Using analogy between travelling waves and heteroclinic solutions of corresponding ODEs, we employ the geometric singular perturbation theory to prove the persistence of these waves when the influence of long-range effects is small. When the long-range diffusion coefficient becomes larger, the behaviour of travelling waves can only be studied numerically. In this case we find that starting with some values, solutions of the model lose monotonicity and become oscillatory.
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Publication status
- Published
Journal
Physics Letters AISSN
0375-9601External DOI
Issue
6Volume
373Page range
668-674Pages
7.0Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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