Isolated periodic wave trains in a generalized Burgers-Huxley equation

Wang Qinlong and Xiong Yu’e and Huang Wentao and Romanovski Valery G.: Isolated periodic wave trains in a generalized Burgers-Huxley equation. (2022)

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We study the isolated periodic wave trains in a class of modified generalized Burgers–Huxley equation. The planar systems with a degenerate equilibrium arising after the traveling transformation are investigated. By finding certain positive definite Lyapunov functions in the neighborhood of the degenerate singular points and the Hopf bifurcation points, the number of possible limit cycles in the corresponding planar systems is determined. The existence of isolated periodic wave trains in the equation is established, which is universal for any positive integer n in this model. Within the process, one interesting example is obtained, namely a series of limit cycles bifurcating from a semi-hyperbolic singular point with one zero eigenvalue and one non-zero eigenvalue for its Jacobi matrix.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 4
ISSN: 1417-3875
Number of Pages: 16
Language: English
Place of Publication: Szeged
DOI: 10.14232/ejqtde.2022.1.4
Uncontrolled Keywords: Burgers-Huxley egyenlet, Differenciálegyenlet
Additional Information: Bibliogr.: p. 13-16. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. May. 23. 15:06
Last Modified: 2022. May. 23. 15:06

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