Generalized conditional symmetries of evolution equations

Abstract

We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector fields in involution. Earlier results on the connection between generalized conditional invariance and generalized reduction of evolution equations are revisited. This leads to a no-go theorem on determining equations for operators of generalized conditional symmetry. It is also shown that up to certain equivalences there exists a one-to-one correspondence between generalized conditional symmetries of an evolution equation and parametric families of its solutions.

23 pages, extended version

References in corpus (3)

• Singular reduction operators in two dimensions
• Group Analysis of Variable Coefficient Diffusion-Convection Equations. II. Contractions and Exact Solutions
• Reduction operators of variable coefficient semilinear diffusion equations with an exponential source

Cited by in corpus (7)

• Group analysis of general Burgers-Korteweg-de Vries equations
• Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
• Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
• Reduction operators of Burgers equation
• Solvable structures for evolution PDEs admitting differential constraints
• Non-point symmetry reduction method of partial differential equations
• Lie-Bäcklund symmetry and non-invariant solutions of nonlinear evolution equations