Approximation of the thermodynamic limit of finite-gap solutions of the focusing NLS hierarchy by multisoliton solutions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914922706763776 |
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| author | Jenkins, Robert Tovbis, Alexander |
| author_facet | Jenkins, Robert Tovbis, Alexander |
| contents | In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (fNLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach. Moreover, we show that both the finite-gap and multisoliton solutions are approximated in the thermodynamic limit by a generalization of the primitive potentials introduced by V. Zakharov and his collaborators in the KdV context. Under certain assumptions on the spectral data for the finite gap potentials, we provide error estimates for the approximation on compact subsets of the $(x,t)$-plane. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of the thermodynamic limit of finite-gap solutions of the focusing NLS hierarchy by multisoliton solutions Jenkins, Robert Tovbis, Alexander Exactly Solvable and Integrable Systems Mathematical Physics 35Q15, 35Q55 In this paper we approximate the thermodynamic limit of finite-gap solutions to any integrable equations in the focusing NLS hierarchy (fNLS, mKdV, ...) with an associated multisoliton solutions using the Riemann-Hilbert Problem approach. Moreover, we show that both the finite-gap and multisoliton solutions are approximated in the thermodynamic limit by a generalization of the primitive potentials introduced by V. Zakharov and his collaborators in the KdV context. Under certain assumptions on the spectral data for the finite gap potentials, we provide error estimates for the approximation on compact subsets of the $(x,t)$-plane. |
| title | Approximation of the thermodynamic limit of finite-gap solutions of the focusing NLS hierarchy by multisoliton solutions |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics 35Q15, 35Q55 |
| url | https://arxiv.org/abs/2408.13700 |