On Quasi-integrable Deformation Scheme of The KdV System
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866917903712911360 |
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| author | Abhinav, Kumar Guha, Partha |
| author_facet | Abhinav, Kumar Guha, Partha |
| contents | We put forward a general approach to quasi-deform the KdV equation by deforming the corresponding Hamiltonian. Following the standard Abelianization process based on the inherent $sl(2)$ loop algebra, an infinite number of anomalous conservation laws are obtained, which yield conserved charges if the deformed solution has definite space-time parity. Judicious choice of the deformed Hamiltonian leads to an integrable system with scaled parameters as well as to a hierarchy of deformed systems, some of which possibly being quasi-integrable. As a particular case, one such deformed KdV system maps to the known quasi-NLS soliton in the already known weak-coupling limit, whereas a generic scaling of the KdV amplitude $u \to u^{1+ε}$ also goes to possible quasi-integrability under an order-by-order expansion. Following a generic parity analysis of the deformed system, these deformed KdV solutions need to be parity-even for quasi-conservation which may be the case here following our analytical approach. From the established quasi-integrability of RLW and mRLW systems [Nucl. Phys. B 939 (2019) 49-94], which are particular cases of the present approach, exact solitons of the quasi-KdV system could be obtained numerically. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_09881 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Quasi-integrable Deformation Scheme of The KdV System Abhinav, Kumar Guha, Partha Exactly Solvable and Integrable Systems Mathematical Physics We put forward a general approach to quasi-deform the KdV equation by deforming the corresponding Hamiltonian. Following the standard Abelianization process based on the inherent $sl(2)$ loop algebra, an infinite number of anomalous conservation laws are obtained, which yield conserved charges if the deformed solution has definite space-time parity. Judicious choice of the deformed Hamiltonian leads to an integrable system with scaled parameters as well as to a hierarchy of deformed systems, some of which possibly being quasi-integrable. As a particular case, one such deformed KdV system maps to the known quasi-NLS soliton in the already known weak-coupling limit, whereas a generic scaling of the KdV amplitude $u \to u^{1+ε}$ also goes to possible quasi-integrability under an order-by-order expansion. Following a generic parity analysis of the deformed system, these deformed KdV solutions need to be parity-even for quasi-conservation which may be the case here following our analytical approach. From the established quasi-integrability of RLW and mRLW systems [Nucl. Phys. B 939 (2019) 49-94], which are particular cases of the present approach, exact solitons of the quasi-KdV system could be obtained numerically. |
| title | On Quasi-integrable Deformation Scheme of The KdV System |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2102.09881 |