Solitary waves and shock waves of the KdV6 equation

•Studied the KdV6 equation.•Both constant and time-dependent coefficients were considered.•Obtained solitons and shock wave solutions.•Numerical simulations are given.

In this work, two variants of the KdV6 equation are investigated. The first variant is a family of the KdV6 equation with arbitrary constant coefficients. The second variant is a KdV6 equation with time-varying coupling coefficients, power law nonlinearity and linear damping term. We make use of the soliton ansatz to determine the solitary wave as well as shock wave solutions for first model and the conditions of existence of solitons are presented. We proved the existence of soliton solutions for a generalized form of KdV6 equation with time-dependent coefficients under specific conditions.