Enhanced group classification and conservation laws of variable coefficient diffusion-convection equations

Abstract:
A class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations is investigated. 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 gauge equivalence transformations. For the class under consideration the complete group classification is performed with respect to extended equivalence group and with respect to the set of all local transformations. Then, using the most direct method, we carry out two classifications of local conservation laws up to equivalence relations generated by both usual and enhanced equivalence groups. Equivalence with respect to enhanced equivalence group and correct choice of gauging coefficients of equations play the major role for simple and clear formulation of the final results.