Integrability structures of the generalized Hunter–Saxton equation

Integrability structures of the generalized Hunter–Saxton equation

We consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existen...

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Veröffentlicht in:Analysis and mathematical physics 2021-06, Vol.11 (2), Article 50
1. Verfasser: Morozov, Oleg I.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Integral equations
Lie groups
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Zusammenfassung:We consider integrability structures of the generalized Hunter–Saxton equation. We obtain the Lax representation with non-removable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate an infinite-dimensional Lie algebra of higher symmetries, and prove existence of infinite number of cosymmetries of higher order. Further, we give examples of employing the higher order symmetries to constructing exact globally defined solutions for the generalized Hunter–Saxton equation.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-021-00490-8