Persistence of travelling waves in a generalized Fisher equation

Kyrychko, Yuliya N and Blyuss, Konstantin B (2009) Persistence of travelling waves in a generalized Fisher equation. Physics Letters A, 373 (6). pp. 668-674. ISSN 0375-9601

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Yuliya Kyrychko
Date Deposited: 06 Feb 2012 20:48
Last Modified: 11 Apr 2012 08:17
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