Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories
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 t...
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MDPI AG
2025-05-01
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| author | Harold Blas |
| author_facet | Harold Blas |
| author_sort | Harold Blas |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-2167c6946ea141e28a6e35eeb4164a49 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-2167c6946ea141e28a6e35eeb4164a492025-08-20T03:14:35ZengMDPI AGMathematics2227-73902025-05-011310156410.3390/math13101564Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton TheoriesHarold Blas0Instituto de Física, Universidade Federal de Mato Grosso, Av. Fernando Correa No. 2367, Bairro Boa Esperança, Cuiabá 78060-900, MT, BrazilThis 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.https://www.mdpi.com/2227-7390/13/10/1564solitonsquasi-integrabilityRiccati-type pseudo-potentialssine-GordonNLSKdV |
| spellingShingle | Harold Blas Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories Mathematics solitons quasi-integrability Riccati-type pseudo-potentials sine-Gordon NLS KdV |
| title | Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories |
| title_full | Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories |
| title_fullStr | Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories |
| title_full_unstemmed | Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories |
| title_short | Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories |
| title_sort | riccati type pseudo potential approach to quasi integrability of deformed soliton theories |
| topic | solitons quasi-integrability Riccati-type pseudo-potentials sine-Gordon NLS KdV |
| url | https://www.mdpi.com/2227-7390/13/10/1564 |
| work_keys_str_mv | AT haroldblas riccatitypepseudopotentialapproachtoquasiintegrabilityofdeformedsolitontheories |