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The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
- Source :
- Nonlinearity 23 (2010) 2009-2028
- Publication Year :
- 2010
-
Abstract
- In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive relation, we explicitly generate infinitely many higher order conserved densities dependent on arbitrary parameters. We find three Nijenhuis recursion operators resulting from Hamiltonian pairs, of which two are new. They generate three hierarchies of commuting local symmetries. Finally, we give a local recursion operator depending on an arbitrary parameter. As a by-product, we classify all anti-symmetric operators of a definite form that are compatible with the Hamiltonian operator $D_x^{-1}$.
- Subjects :
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
37K05, 37K10, 35Q53
Subjects
Details
- Database :
- arXiv
- Journal :
- Nonlinearity 23 (2010) 2009-2028
- Publication Type :
- Report
- Accession number :
- edsarx.1008.3085
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/0951-7715/23/8/011