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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06458 |
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| _version_ | 1866911756158238720 |
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| author | Zhang, Hongyi Zhang, Yufeng Feng, Binlu |
| author_facet | Zhang, Hongyi Zhang, Yufeng Feng, Binlu |
| contents | We investigate the Cauchy problem of a new higher-order nonlinear Schrödinger equation (NHNSE) with weighted Sobolev initial data which is derived by ourselves. By applying $\bar{\partial}$-steepest descent method, we derive the long-time asymptotics of the NHNSE. Explicit steps are as follows: first of all, based on the spectral analysis of a Lax pair and scattering matrice, the solution of the NHNSE is exhibted through solving the corresponding Riemann-Hilbert problem. Secondly, by applying some properties of the Riemann-Hilbert problem, we obtain the long-time asymptotics of the solution to the NHNSE. As we know that the properties of the NHNSE presented in the paper have not been found in any scholar journals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior for a new higher-order nonlinear Schrödinger equation Zhang, Hongyi Zhang, Yufeng Feng, Binlu Analysis of PDEs Mathematical Physics We investigate the Cauchy problem of a new higher-order nonlinear Schrödinger equation (NHNSE) with weighted Sobolev initial data which is derived by ourselves. By applying $\bar{\partial}$-steepest descent method, we derive the long-time asymptotics of the NHNSE. Explicit steps are as follows: first of all, based on the spectral analysis of a Lax pair and scattering matrice, the solution of the NHNSE is exhibted through solving the corresponding Riemann-Hilbert problem. Secondly, by applying some properties of the Riemann-Hilbert problem, we obtain the long-time asymptotics of the solution to the NHNSE. As we know that the properties of the NHNSE presented in the paper have not been found in any scholar journals. |
| title | Asymptotic behavior for a new higher-order nonlinear Schrödinger equation |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2401.06458 |