Partial and complete linearization of PDEs based on conservation laws

Please always quote using this URN: urn:nbn:de:0297-zib-8409

A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (-system) if that is possible. Infinite parameter conservation laws can be computed, for example, with the computer algebra package {\sc ConLaw}.

Metadaten
Author:	Thomas Wolf
Document Type:	ZIB-Report
MSC-Classification:	35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A30 Geometric theory, characteristics, transformations [See also 58J70, 58J72]
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J70 Invariance and symmetry properties [See also 35A30]
	58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J72 Correspondences and other transformation methods (e.g. Lie- Bäcklund) [See also 35A22]
	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
Date of first Publication:	2005/01/14
Series (Serial Number):	ZIB-Report (05-06)
ArXiv Id:	http://arxiv.org/abs/nlin.SI/0501034
ZIB-Reportnumber:	05-06
Published in:	Appeared in: Trends in Mathematics: Differential Equations with Symbolic Computation. Eds. Dongming Wang, Zhiming Zheng (2005) Birkhäuser, pp. 291-306

Open Access