College of Mathematics and Statistics
Northwest Normal University
Lanzhou 730070, China
email: haoyx23@nwnu.edu.cn
College of Mathematics and Statistics
Northwest Normal University
Lanzhou 730070, China
email: 166473086@qq.com
Yu-Xia Hao, Zi-Ming Liu
Abstract:
In this work we study the traveling wave solutions for a generalized nonlocal
dispersal Leslie-Gower predator-prey system. Employing the truncation method and
Schauder fixed-point theorem, we establish the existence of traveling waves
connecting the semi-trivial equilibrium to the coexistence equilibrium for all wave
speeds \(c \geq c^*\), where \(c^*\) denotes the minimal wave speed. Particularly,
the right-hand tail limit of the wave profile is obtained by using the idea of a
contracting rectangle. Meanwhile, by analyzing the characteristic equation
obtained from linearizing the system at the semi-trivial equilibrium, we showed
the nonexistence of traveling waves for \(0< c< c_* \).
The main technical challenges arise from the combined effects of nonlocal dispersal
and the lack of monotonicity in the system.
Submitted March 27, 2026. Published July 8, 2026.
Math Subject Classifications: 35K57, 35R20, 92D25.
Key Words: Leslie-Gower predator-prey system; nonlocal dispersal; traveling wave solution.
DOI: 10.58997/ejde.2026.51
Show me the PDF file (409 KB), TEX file for this article.
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Yu-Xia Hao College of Mathematics and Statistics Northwest Normal University Lanzhou 730070, China email: haoyx23@nwnu.edu.cn |
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Zi-Ming Liu College of Mathematics and Statistics Northwest Normal University Lanzhou 730070, China email: 166473086@qq.com |
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