On form-preserving point transformations of partial differential equations

1998/02/13 by J G Kingston, J. G. Kingston, C. Sophocleous +1 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · doi:10.1088/0305-4470/31/6/010

openalex publication_date 1998/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

New identities are presented relating arbitrary order partial derivatives of and for the general point transformation , . These identities are used to study the nature of those point transformations which preserve the general form of a wide class of 1 + 1 partial differential equations. These results facilitate the search for point symmetries, both discrete and continuous (Lie), and assist the search for point transformations which reduce equations to canonical, but similar, form. A simple test for the existence of hodograph-type transformations between equations of similar form is given.

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• Lie symmetry classification and exact solutions of a diffusive Lotka-Volterra system with convection
• Symmetry classification of third-order nonlinear evolution equations
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. IV. Potential Symmetries
• New results on group classification of nonlinear diffusion–convection equations

Related

• On the point transformations for the second order differential equations. I
• Point-invariant classes of the third order ordinary differential equations
• Symmetry operators and generation of symmetry transformations of partial differential equations
• On equivalence of singularities of linear second order ordinary differential equations by point transformations
• On point transformations of linear equations of maximal symmetry