Some classifications of hyperbolic vector evolution equations

Anco, Stephen; Wolf, Thomas

Some classifications of hyperbolic vector evolution equations

Please always quote using this URN: urn:nbn:de:0297-zib-8429

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several $O(N)$-invariant classes of hyperbolic equations $Utx=f(U,Ut,Ux)$ for an $N$-component vector $U(t,x)$ are considered. In each class we find all scaling-homogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.

Metadaten
Author:	Stephen Anco, Thomas Wolf
Document Type:	ZIB-Report
MSC-Classification:	70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Sxx Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83- XX] / 70S10 Symmetries and conservation laws
PACS-Classification:	00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.70.-c Computational techniques; simulations (for quantum computation, see 03.67.Lx; for computational techniques extensively used in subdivisions of physics, see the appropriate section; for example, see 47.11.-j Computational methods in fluid dynamics) / 02.70.Wz Symbolic computation (computer algebra)
	40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 45.00.00 Classical mechanics of discrete systems / 45.20.-d Formalisms in classical mechanics / 45.20.Jj Lagrangian and Hamiltonian mechanics
	40.00.00 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS / 45.00.00 Classical mechanics of discrete systems / 45.40.-f Dynamics and kinematics of rigid bodies / 45.40.Cc Rigid body and gyroscope motion
Date of first Publication:	2005/01/14
Series (Serial Number):	ZIB-Report (05-08)
ArXiv Id:	http://arxiv.org/abs/nlin.SI/0412015
ZIB-Reportnumber:	05-08
Published in:	Appeared under the title "Some symmetry classifications of hyperbolic vector evolution equations" in: Journal of Nonl. Math. Physics, Vol. 12, no. 4 (2005), pp. 607-608.

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Some classifications of hyperbolic vector evolution equations

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