Symmetry-based algorithms to relate partial differential equations. II: Linearization by nonlocal symmetries. (English) Zbl 0718.35004

Bluman, G. W.; Kumei, S.

Eur. J. Appl. Math. 1, No. 3, 217-223 (1990).

[For part I see ibid., 189-216 (1990; Zbl 0718.35003).]
An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations.

Reviewer: G.W.Bluman

MSC:

35A30	Geometric theory, characteristics, transformations in context of PDEs
35G20	Nonlinear higher-order PDEs
35K55	Nonlinear parabolic equations

Keywords:

linearization; nonlocal symmetries; Hopf-Cole transformation

Citations:

Zbl 0718.35003

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