ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The simplest generalization of the intermediate long-wave hierarchy (ILW) is considered to show how to extend the Zakharov–Shabat dressing method to nonlocal, i.e., integro-partial differential, equations. The purpose is to give a procedure of constructing the zero-curvature representation of this class of equations. This result obtains by combining the Drinfeld–Sokolov formalism together with the introduction of an operator-valued spectral parameter, namely, a spectral parameter that does not commute with the space variable x. This extension provides a connection between the ILWk hierarchy and the Saveliev–Vershik continuum graded Lie algebras. In the case of ILW2 the Fairlie–Zachos sinh-algebra was found.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529876
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