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Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories

Author

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  • Harold Blas

    (Instituto de Física, Universidade Federal de Mato Grosso, Av. Fernando Correa No. 2367, Bairro Boa Esperança, Cuiabá 78060-900, MT, Brazil)

Abstract

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.

Suggested Citation

  • Harold Blas, 2025. "Riccati-Type Pseudo-Potential Approach to Quasi-Integrability of Deformed Soliton Theories," Mathematics, MDPI, vol. 13(10), pages 1-35, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1564-:d:1652592
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