Classical symmetry analysis and exact solutions for generalized Korteweg–de Vries models with variable coefficients

In this paper, by using the classical symmetry analysis method symmetries for the generalized variable-coefficient Korteweg–de Vries model are obtained. Then, the reduced nonlinear ordinary differential equations with variable coefficients are solved by auxiliary equation method. Hermite differential equation is chosen as an auxiliary equation and some new exact solutions for the nonlinear partial differential equation in hand are obtained. © 2018 Elsevier Ltd