Invertible Mappings of Nonlinear PDEs to Linear PDEs Through Admitted Conservation Laws

Please always quote using this URN: urn:nbn:de:0297-zib-10652
  • An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.

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Author:Stephen Anco, George Bluman, Thomas Wolf
Document Type:ZIB-Report
Tag:conservation laws; linearization; symmetries
MSC-Classification:22-XX TOPOLOGICAL GROUPS, LIE GROUPS (For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX) / 22Exx Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90) / 22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties [See also 17B65, 58B25, 58H05]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Axx General topics / 35A30 Geometric theory, characteristics, transformations [See also 58J70, 58J72]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L65 Conservation laws
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]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX) / 70Hxx Hamiltonian and Lagrangian mechanics [See also 37Jxx] / 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
Creating Corporation:Department of Mathematics, Brock University, St. Catharines, ON Canada L2S 3A1
Contributing Corporation:Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2 Canada
Date of first Publication:2008/03/03
Series (Serial Number):ZIB-Report (08-11)
ISSN:1438-0064
ZIB-Reportnumber:08-11
Published in:Appeared in: Acta Applicandae Mathematicae Volume 101, Numbers 1-3 (2008), pp. 21-38
DOI:https://doi.org/10.1007/s10440-008-9205-7