On Quasi-integrable Deformation Scheme of The KdV System

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 → u1+ 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. Mathematics Subject Classifications (2010): 37K10, 37K55. 37K30.

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