Solitary wave solutions of the delayed KP-BBM equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929347760226304 |
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| author | Xia, Yonghui Zhang, Haojie Zheng, Hang |
| author_facet | Xia, Yonghui Zhang, Haojie Zheng, Hang |
| contents | In this paper, we consider a kind of shallow water wave model called the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. We firstly consider the unperturbed KP-BBM equation. Then by using the geometric singular perturbation (GSP) theory, especially the invariant manifold theory, method of dynamical system and Melnikov function, the existence of solitary wave solutions of perturbed KP-BBM equation is proved. In other words, we dissuss the equation under different nonlinear terms. Finally, we validate our results with numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solitary wave solutions of the delayed KP-BBM equation Xia, Yonghui Zhang, Haojie Zheng, Hang Analysis of PDEs Classical Analysis and ODEs In this paper, we consider a kind of shallow water wave model called the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. We firstly consider the unperturbed KP-BBM equation. Then by using the geometric singular perturbation (GSP) theory, especially the invariant manifold theory, method of dynamical system and Melnikov function, the existence of solitary wave solutions of perturbed KP-BBM equation is proved. In other words, we dissuss the equation under different nonlinear terms. Finally, we validate our results with numerical simulations. |
| title | Solitary wave solutions of the delayed KP-BBM equation |
| topic | Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2404.01005 |