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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 Blyuss
Travelling 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.

History

Publication status

  • Published

Journal

Physics Letters A

ISSN

0375-9601

Issue

6

Volume

373

Page range

668-674

Pages

7.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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