On quasi-integrable deformation scheme of the KdV system
Abstract We propose a general approach to quasi-deform the Korteweg–De Vries (KdV) equation by deforming its Hamiltonian. The standard abelianization process based on the inherent sl(2) loop algebra leads to an infinite number of anomalous conservation laws, that yield conserved charges for definite...
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Nature Portfolio
2025-01-01
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| Online Access: | https://doi.org/10.1038/s41598-025-86381-5 |
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| author | Kumar Abhinav Partha Guha |
| author_facet | Kumar Abhinav Partha Guha |
| author_sort | Kumar Abhinav |
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| description | Abstract We propose a general approach to quasi-deform the Korteweg–De Vries (KdV) equation by deforming its Hamiltonian. The standard abelianization process based on the inherent sl(2) loop algebra leads to an infinite number of anomalous conservation laws, that yield conserved charges for definite space-time parity of the solution. Judicious choice of the deformed Hamiltonian yields an integrable system with scaled parameters as well as a hierarchy of deformed systems, some of which possibly are quasi-integrable. One such system maps to the known quasi-deformed nonlinear Schrödinger (NLS) soliton in the already known weak-coupling limit, whereas a generic scaling of the KdV amplitude $$u\rightarrow u^{1+\varepsilon }$$ also suggests quasi-integrability under an order-by-order expansion. In general, these deformed KdV solutions need to be parity-even for quasi-conservation that agrees with our analytical results. Following the recent demonstration of quasi-integrability in regularized long wave (RLW) and modified regularized long wave (mRLW) systems by ter Braak et al. (Nucl Phys B 939:49–94, 2019), that are particular cases of the present approach, general soliton solutions should numerically be accessible. |
| format | Article |
| id | doaj-art-194b360e5a0b43e3bf37035b24d7a3cf |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-194b360e5a0b43e3bf37035b24d7a3cf2025-01-19T12:18:00ZengNature PortfolioScientific Reports2045-23222025-01-0115111810.1038/s41598-025-86381-5On quasi-integrable deformation scheme of the KdV systemKumar Abhinav0Partha Guha1Centre for Theoretical Physics and Natural Philosophy, Nakhonsawan Studiorum for Advanced Studies, Mahidol UniversityDepartment of Mathematics, Khalifa University of Science and TechnologyAbstract We propose a general approach to quasi-deform the Korteweg–De Vries (KdV) equation by deforming its Hamiltonian. The standard abelianization process based on the inherent sl(2) loop algebra leads to an infinite number of anomalous conservation laws, that yield conserved charges for definite space-time parity of the solution. Judicious choice of the deformed Hamiltonian yields an integrable system with scaled parameters as well as a hierarchy of deformed systems, some of which possibly are quasi-integrable. One such system maps to the known quasi-deformed nonlinear Schrödinger (NLS) soliton in the already known weak-coupling limit, whereas a generic scaling of the KdV amplitude $$u\rightarrow u^{1+\varepsilon }$$ also suggests quasi-integrability under an order-by-order expansion. In general, these deformed KdV solutions need to be parity-even for quasi-conservation that agrees with our analytical results. Following the recent demonstration of quasi-integrability in regularized long wave (RLW) and modified regularized long wave (mRLW) systems by ter Braak et al. (Nucl Phys B 939:49–94, 2019), that are particular cases of the present approach, general soliton solutions should numerically be accessible.https://doi.org/10.1038/s41598-025-86381-5KdV equationNLS equationIntegrabilityQuasi-integrable deformation |
| spellingShingle | Kumar Abhinav Partha Guha On quasi-integrable deformation scheme of the KdV system Scientific Reports KdV equation NLS equation Integrability Quasi-integrable deformation |
| title | On quasi-integrable deformation scheme of the KdV system |
| title_full | On quasi-integrable deformation scheme of the KdV system |
| title_fullStr | On quasi-integrable deformation scheme of the KdV system |
| title_full_unstemmed | On quasi-integrable deformation scheme of the KdV system |
| title_short | On quasi-integrable deformation scheme of the KdV system |
| title_sort | on quasi integrable deformation scheme of the kdv system |
| topic | KdV equation NLS equation Integrability Quasi-integrable deformation |
| url | https://doi.org/10.1038/s41598-025-86381-5 |
| work_keys_str_mv | AT kumarabhinav onquasiintegrabledeformationschemeofthekdvsystem AT parthaguha onquasiintegrabledeformationschemeofthekdvsystem |