Non-Monotone Traveling Waves of the Weak Competition Lotka-Volterra System
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| Format: | Preprint |
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2025
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| _version_ | 1866912981069070336 |
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| author | Chen, Chiun-Chuan Hsiao, Ting-Yang Wang, Shun-Chieh |
| author_facet | Chen, Chiun-Chuan Hsiao, Ting-Yang Wang, Shun-Chieh |
| contents | We investigate traveling wave solutions in the two-species reaction-diffusion Lotka-Volterra competition system under weak competition. For the strict weak competition regime $(b<a<1/c,\,d>0)$, we construct refined upper and lower solutions combined with the Schauder fixed point theorem to establish the existence of traveling waves for all wave speeds $s\geq s^*:=\max\{2,2\sqrt{ad}\}$, and provide verifiable sufficient conditions for the emergence of non-monotone waves. Such conditions for non-monotonic waves have not been explicitly addressed in previous studies. It is interesting to point out that our result for non-monotone waves also hold for the critical speed case $s=s^*$. In addition, in the critical weak competition case $(b<a=1/c,\,d>0)$, we rigorously prove, for the first time, the existence of front-pulse traveling waves. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_04501 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Monotone Traveling Waves of the Weak Competition Lotka-Volterra System Chen, Chiun-Chuan Hsiao, Ting-Yang Wang, Shun-Chieh Analysis of PDEs Dynamical Systems Populations and Evolution We investigate traveling wave solutions in the two-species reaction-diffusion Lotka-Volterra competition system under weak competition. For the strict weak competition regime $(b<a<1/c,\,d>0)$, we construct refined upper and lower solutions combined with the Schauder fixed point theorem to establish the existence of traveling waves for all wave speeds $s\geq s^*:=\max\{2,2\sqrt{ad}\}$, and provide verifiable sufficient conditions for the emergence of non-monotone waves. Such conditions for non-monotonic waves have not been explicitly addressed in previous studies. It is interesting to point out that our result for non-monotone waves also hold for the critical speed case $s=s^*$. In addition, in the critical weak competition case $(b<a=1/c,\,d>0)$, we rigorously prove, for the first time, the existence of front-pulse traveling waves. |
| title | Non-Monotone Traveling Waves of the Weak Competition Lotka-Volterra System |
| topic | Analysis of PDEs Dynamical Systems Populations and Evolution |
| url | https://arxiv.org/abs/2510.04501 |