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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.05890 |
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| _version_ | 1866913800770289664 |
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| author | Blas, Harold |
| author_facet | Blas, Harold |
| contents | This review paper explores the Riccati-type pseudo-potential formulation applied to the quasi-integrable sine-Gordon, KdV, and NLS models. The proposed framework provides a unified methodology for analyzing quasi-integrability properties across various integrable systems, including deformations of the sine-Gordon, Bullough-Dodd, Toda, KdV, pKdV, NLS and SUSY sine-Gordon models. Key findings include the emergence of infinite towers of anomalous conservation laws within the Riccati-type approach and the identification of exact non-local conservation laws in the linear formulations of deformed models. As modified integrable models play a crucial role in diverse fields of nonlinear physics-such as Bose-Einstein condensation, superconductivity, gravity models, optics and soliton turbulence-these results may have far-reaching applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories Blas, Harold High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems This review paper explores the Riccati-type pseudo-potential formulation applied to the quasi-integrable sine-Gordon, KdV, and NLS models. The proposed framework provides a unified methodology for analyzing quasi-integrability properties across various integrable systems, including deformations of the sine-Gordon, Bullough-Dodd, Toda, KdV, pKdV, NLS and SUSY sine-Gordon models. Key findings include the emergence of infinite towers of anomalous conservation laws within the Riccati-type approach and the identification of exact non-local conservation laws in the linear formulations of deformed models. As modified integrable models play a crucial role in diverse fields of nonlinear physics-such as Bose-Einstein condensation, superconductivity, gravity models, optics and soliton turbulence-these results may have far-reaching applications. |
| title | Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories |
| topic | High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2503.05890 |