Exponential and algebraic double-soliton solutions of the massive Thirring model
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929609664102400 |
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| author | Li, Zhi-Qiang Pelinovsky, Dmitry E. Tian, Shou-Fu |
| author_facet | Li, Zhi-Qiang Pelinovsky, Dmitry E. Tian, Shou-Fu |
| contents | The newly discovered exponential and algebraic double-soliton solutions of the massive Thirring model in laboratory coordinates are placed in the context of the inverse scattering transform. We show that the exponential double-solitons correspond to double isolated eigenvalues in the Lax spectrum, whereas the algebraic double-solitons correspond to double embedded eigenvalues on the imaginary axis, where the continuous spectrum resides. This resolves the long-standing conjecture that multiple embedded eigenvalues may exist in the spectral problem associated with the massive Thirring model. To obtain the exponential double-solitons, we solve the Riemann--Hilbert problem with the reflectionless potential in the case of a quadruplet of double poles in each quadrant of the complex plane. To obtain the algebraic double-solitons, we consider the singular limit where the quadruplet of double poles degenerates into a symmetric pair of double embedded poles on the imaginary axis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential and algebraic double-soliton solutions of the massive Thirring model Li, Zhi-Qiang Pelinovsky, Dmitry E. Tian, Shou-Fu Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons The newly discovered exponential and algebraic double-soliton solutions of the massive Thirring model in laboratory coordinates are placed in the context of the inverse scattering transform. We show that the exponential double-solitons correspond to double isolated eigenvalues in the Lax spectrum, whereas the algebraic double-solitons correspond to double embedded eigenvalues on the imaginary axis, where the continuous spectrum resides. This resolves the long-standing conjecture that multiple embedded eigenvalues may exist in the spectral problem associated with the massive Thirring model. To obtain the exponential double-solitons, we solve the Riemann--Hilbert problem with the reflectionless potential in the case of a quadruplet of double poles in each quadrant of the complex plane. To obtain the algebraic double-solitons, we consider the singular limit where the quadruplet of double poles degenerates into a symmetric pair of double embedded poles on the imaginary axis. |
| title | Exponential and algebraic double-soliton solutions of the massive Thirring model |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2412.00838 |