On quasi-integrable deformation scheme of the KdV system
Issued Date
2025-01-18
Resource Type
eISSN
20452322
Scopus ID
2-s2.0-85216440238
Pubmed ID
39827181
Journal Title
Scientific reports
Volume
15
Issue
1
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SCOPUS
Bibliographic Citation
Scientific reports Vol.15 No.1 (2025) , 2402
Suggested Citation
Abhinav K., Guha P. On quasi-integrable deformation scheme of the KdV system. Scientific reports Vol.15 No.1 (2025) , 2402. doi:10.1038/s41598-025-86381-5 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/104258
Title
On quasi-integrable deformation scheme of the KdV system
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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 [Formula: see text] 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.