Group Analysis of Variable Coefficient Diffusion-Convection Equations. I. Enhanced Group Classification

Abstract

We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1+1)-dimensional nonlinear diffusion--convection equations with coefficients depending on the space variable. At first, we construct the usual equivalence group and the extended one including transformations which are nonlocal with respect to arbitrary elements. The extended equivalence group has interesting structure since it contains a non-trivial subgroup of non-local gauge equivalence transformations. The complete group classification of the class under consideration is carried out with respect to the extended equivalence group and with respect to the set of all point transformations. Usage of extended equivalence and correct choice of gauges of arbitrary elements play the major role for simple and clear formulation of the final results. The set of admissible transformations of this class is preliminary investigated.

25 pages

References in corpus (5)

• Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations
• New results on group classification of nonlinear diffusion-convection equations
• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Potential equivalence transformations for nonlinear diffusion-convection equations
• Group classification of (1+1)-Dimensional Schrödinger Equations with Potentials and Power Nonlinearities

Cited by in corpus (18)

• Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
• Complete group classification of a class of nonlinear wave equations
• Equivalence transformations in the study of integrability
• Enhanced preliminary group classification of a class of generalized diffusion equations
• Symmetry preserving parameterization schemes
• Lie symmetries and exact solutions of variable coefficient mKdV equations: an equivalence based approach
• Symbolic Computation of Equivalence Transformations and Parameter Reduction for Nonlinear Physical Models
• Generalization of the algebraic method of group classification with application to nonlinear wave and elliptic equations
• Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusion
• Lie symmetries of two-dimensional shallow water equations with variable bottom topography
• Extended symmetry analysis of generalized Burgers equations
• Group classification of variable coefficient generalized Kawahara equations
• Group Classification of a Generalized Black--Scholes--Merton Equation
• Group classification of variable coefficient KdV-like equations
• Mapping method of group classification
• Group Classification of a generalization of the Heath Equation
• Equivalence groupoid of generalized potential Burgers equations
• Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid