The tanh method for a reliable treatment of the K(n, n) and the KP(n, n) equations and its variants

In this work, the nonlinear K(n, n) and KP(n, n) equations and its variants are analytically studied. We show that these equations may exhibit compactons, solitons or periodic solutions by using the tanh method. The analysis reveals the change of the physical structure of the solutions as a result of the exponents and the coefficients of the derivatives.