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Poisson structure of a modified Hunter-Saxton equation
University of Cambridge, United Kingdom .ORCID iD: 0000-0001-6191-7769
2008 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 41, no 28, 285207Article in journal (Refereed) Published
Abstract [en]

Both the well-known Korteweg-de Vries equation and the Hunter-Saxton equation with a linear wux-term, -utxx = -2ωu x + 2uxuxx + uuxxx, ω > 0, are bi-Hamiltonian in the sense that each equation is Hamiltonian with respect to two compatible, but distinct, Poisson brackets. We present a nonlinear change of variables which maps between the two bi-Poisson structures, giving a correspondence between the infinite hierarchies of conservation laws and commuting flows associated with the equations. In particular, under this change of variables this (modified) Hunter-Saxton equation can be viewed as a member of the KdV hierarchy.

Place, publisher, year, edition, pages
2008. Vol. 41, no 28, 285207
National Category
Mathematics Physical Sciences
URN: urn:nbn:se:kth:diva-163829DOI: 10.1088/1751-8113/41/28/285207ISI: 000257167100017ScopusID: 2-s2.0-52349101360OAI: diva2:802364

QC 20150427

Available from: 2015-04-12 Created: 2015-04-12 Last updated: 2015-04-27Bibliographically approved

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Lenells, Jonatan
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