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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/2403.12925 |
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| _version_ | 1866911803637760000 |
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| author | Gerdjikov, Vladimir S. Grahovski, Georgi G. |
| author_facet | Gerdjikov, Vladimir S. Grahovski, Georgi G. |
| contents | The paper is devoted to $N$-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators $L$, whose potentials $Q(x,t)$ tend to constants $Q_\pm$ for $x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral properties of $L$, the direct scattering transform and construct its fundamental analytic solutions. We generalise Wronskian relations for the case of CBC -- this allows us to analyse the mapping between the scattering data and the $x$-derivative of the potential $Q_x$. Next, using the Wronskian relations we derive the dispersion laws for the $N$-wave hierarchy and describe the NLEE related to the given Lax operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $N$-waves hierarchy with constant boundary conditions. Spectral properties Gerdjikov, Vladimir S. Grahovski, Georgi G. Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics The paper is devoted to $N$-wave equations with constant boundary conditions related to symplectic Lie algebras. We study the spectral properties of a class of Lax operators $L$, whose potentials $Q(x,t)$ tend to constants $Q_\pm$ for $x\to \pm \infty$. For special choices of $Q_\pm$ we outline the spectral properties of $L$, the direct scattering transform and construct its fundamental analytic solutions. We generalise Wronskian relations for the case of CBC -- this allows us to analyse the mapping between the scattering data and the $x$-derivative of the potential $Q_x$. Next, using the Wronskian relations we derive the dispersion laws for the $N$-wave hierarchy and describe the NLEE related to the given Lax operator. |
| title | On the $N$-waves hierarchy with constant boundary conditions. Spectral properties |
| topic | Exactly Solvable and Integrable Systems High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2403.12925 |