Acta Applicandae Mathematicae

, Volume 101, Issue 1, pp 21–38

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


  • Stephen Anco
    • Department of MathematicsBrock University
    • Department of MathematicsUniversity of British Columbia
  • Thomas Wolf
    • Department of MathematicsBrock University

DOI: 10.1007/s10440-008-9205-7

Cite this article as:
Anco, S., Bluman, G. & Wolf, T. Acta Appl Math (2008) 101: 21. doi:10.1007/s10440-008-9205-7


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.


Conservation lawsLinearizationSymmetries

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media B.V. 2008