Extended symmetry analysis of generalized Burgers equations

Abstract

Using advanced classification techniques, we carry out the extended symmetry analysis of the class of generalized Burgers equations of the form $u_t+u{u}_x+f(t,x)u_{xx}=0$. This enhances all the previous results on symmetries of these equations and includes the description of admissible transformations, Lie symmetries, Lie and nonclassical reductions, conservation laws, potential admissible transformations and potential symmetries. The study is based on the fact that the class is normalized, and its equivalence group is finite-dimensional.

31 pages, 2 tables, minor corrections

References in corpus (10)

• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
• Potential equivalence transformations for nonlinear diffusion-convection equations
• Reduction Operators of Linear Second-Order Parabolic Equations
• Singular reduction operators in two dimensions
• Local conservation laws of second-order evolution equations
• Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
• Reduction operators of Burgers equation
• Normalized classes of generalized Burgers equations
• Equivalence groupoid of generalized potential Burgers equations

Cited by in corpus (9)

• Point and generalized symmetries of the heat equation revisited
• Extended symmetry analysis of two-dimensional degenerate Burgers equation
• Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
• Extended symmetry analysis of remarkable (1+2)-dimensional Fokker-Planck equation
• Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti-Leon-Pempinelli system
• Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations
• Mapping method of group classification
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Hidden symmetries, hidden conservation laws and exact solutions of dispersionless Nyzhnyk equation