New exact solutions for a generalization of the Korteweg–de Vries equation (KdV6)

The generalized tanh–coth method is used to construct periodic and soliton solutions for a new integrable system, which has been derived from an integrable sixth-order nonlinear wave equation (KdV6). The system is formed by two equations. One of the equations may be considered as a Korteweg–de Vries equation with a source and the second equation is a third-order linear differential equation.