Exact linearization and exact solutions of a generalized Thomas equation with general variable coefficients

Abstract

In this paper, we investigate a generalized Thomas equation with general variable coefficients, which describes the processes in chemical kinetics with ion exchange under sorption in a reagent flow. It is shown that the generalized Thomas equation with variable coefficients can be exactly linearized as long as the variable coefficient functions satisfy some constraint conditions. Firstly, we establish a nonlinear transformation between the generalized Thomas equation with variable coefficients and the linear hyperbolic equation with variable coefficients. Then we obtain a series of explicit exact solutions of the generalized Thomas equation with variable coefficients by solving reduced linear hyperbolic equation with variable coefficients under some coefficient conditions. In some cases, these exact solutions contain an arbitrary function.