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arXiv · 2503.05890

Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories

Harold Blas
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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.

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Harold Blas. 2025-04-20. Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories. https://arxiv.org/abs/2503.05890

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