On a KdV equation with higher-order nonlinearity: Traveling wave solutions

In this work, the improved tanh–coth method is used to obtain wave solutions to a Korteweg–de Vries (KdV) equation with higher-order nonlinearity, from which the standard KdV and the modified Korteweg–de Vries (mKdV) equations with variable coefficients can be derived as particular cases. However, the model studied here include other important equations with applications in several fields of physical and nonlinear sciences. Periodic and soliton solutions are formally derived.