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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Bibliographic Details
Main Author: Harold Blas
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/10/1564
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Summary: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.
ISSN:2227-7390