Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the $L^2$ Space
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| Format: | Preprint |
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2024
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| _version_ | 1866911789015367680 |
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| author | Yang, Yiling Fan, Engui Liu, Yue |
| author_facet | Yang, Yiling Fan, Engui Liu, Yue |
| contents | In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schrödinger equation under perturbations in $L^2(\mathbb{R})$. We demonstrate this stability by utilizing the Bäcklund transformation associated with the Lax pair and by applying the first conservation quantity in $L^2(\mathbb{R}).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the $L^2$ Space Yang, Yiling Fan, Engui Liu, Yue Analysis of PDEs Mathematical Physics 35Q51, 35Q15, 37K15, 35Q35 In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schrödinger equation under perturbations in $L^2(\mathbb{R})$. We demonstrate this stability by utilizing the Bäcklund transformation associated with the Lax pair and by applying the first conservation quantity in $L^2(\mathbb{R}).$ |
| title | Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the $L^2$ Space |
| topic | Analysis of PDEs Mathematical Physics 35Q51, 35Q15, 37K15, 35Q35 |
| url | https://arxiv.org/abs/2402.16222 |