Reduction operators of Burgers equation

Abstract

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

11 pages, minor corrections

References in corpus (5)

• A precise definition of reduction of partial differential equations
• Symmetry reduction and exact solutions of the Navier-Stokes equations
• Generalized conditional symmetries of evolution equations
• Reduction Operators of Linear Second-Order Parabolic Equations
• Singular reduction operators in two dimensions

Cited by in corpus (5)

• Point and generalized symmetries of the heat equation revisited
• Enhanced symmetry analysis of two-dimensional Burgers system
• Extended symmetry analysis of generalized Burgers equations
• Singular reduction modules of differential equations
• Analytical and numerical studying of the perturbed Korteweg--de Vries equation