Reduction operators and exact solutions of generalized Burgers equations

Abstract

Reduction operators of generalized Burgers equations are studied. A connection between these equations and potential fast diffusion equations with power nonlinearity -1 via reduction operators is established. Exact solutions of generalized Burgers equations are constructed using this connection and known solutions of the constant-coefficient potential fast diffusion equation.

7 pages

References in corpus (3)

• Reduction Operators of Linear Second-Order Parabolic Equations
• Singular reduction operators in two dimensions
• On nonclassical symmetries of generalized Huxley equations

Cited by in corpus (9)

• Group analysis of general Burgers-Korteweg-de Vries equations
• Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method
• Group classification and exact solutions of variable-coefficient generalized Burgers equations with linear damping
• Extended symmetry analysis of generalized Burgers equations
• Extended symmetry analysis of two-dimensional degenerate Burgers equation
• Singular reduction modules of differential equations
• Normalized classes of generalized Burgers equations
• Group analysis of variable coefficient generalized fifth-order KdV equations
• Equivalence groupoid of generalized potential Burgers equations