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Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws
- Source :
- Int. J. Mod. Phys. B36 (2022) 2250070
- Publication Year :
- 2022
-
Abstract
- A dual Riccati-type pseudo-potential formulation is introduced for a modified AKNS system (MAKNS) and infinite towers of novel anomalous conservation laws are uncovered. In addition, infinite towers of exact non-local conservation laws are uncovered in a linear formulation of the system. It is shown that certain modifications of the non-linear Schr\"odinger model (MNLS) can be obtained through a reduction process starting from the MAKNS model. So, the novel infinite sets of quasi-conservation laws and related anomalous charges are constructed by an unified and rigorous approach based on the Riccati-type pseudo-potential method, for the standard NLS and modified MNLS cases, respectively. The non-local properties, the complete list of towers of infinite number of anomalous charges and the (non-local) exact conservation laws of the quasi-integrable systems, such as the deformed Bullough-Dodd, Toda, KdV and SUSY sine-Gordon systems can be studied in the framework presented in this paper. Our results may find many applications since the AKNS-type system arises in several branches of non-linear physics, such as Bose-Einstein condensation, superconductivity and soliton turbulence.<br />Comment: 26 pages, LaTex. arXiv admin note: substantial text overlap with arXiv:2007.13910
Details
- Database :
- arXiv
- Journal :
- Int. J. Mod. Phys. B36 (2022) 2250070
- Publication Type :
- Report
- Accession number :
- edsarx.2203.14745
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0217979222500709