The tanh–coth method for new compactons and solitons solutions for the K(n, n) and the K(n + 1, n + 1) equations

The nonlinear K(n, n) and the K(n + 1, n + 1) equations are analytically studied. The tanh–coth method, the rational hyperbolic functions method, and the rational exponential function method are applied for this analytic study. We show that these equations exhibit new compactons, solitons and periodic solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.