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

Harold Blas ()
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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

Mathematics, 2025, vol. 13, issue 10, 1-35

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.

Keywords: solitons; quasi-integrability; Riccati-type pseudo-potentials; sine-Gordon; NLS; KdV (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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