Computations of soliton solutions and periodic solutions for the focusing branch of the nonlinear dispersive K(n, n) equations in higher-dimensional spaces

In the present paper, the focusing branch of the genuinely nonlinear dispersive K(n, n) equation is studied in one-, two- and three-dimensional spaces in the case of 0 < n < 1. When n=12 and 13, traveling solitary wave solutions and periodic solutions are computed by using the tanh method and hyperbolic function method, respectively. Then we generalize the results to the case n=kk+2(k∈N) and general formulas for exact solutions of K(n, n) equation are established, which indicate that under appropriate conditions, traveling solitary wave solutions and periodic solutions of the focusing branch of the genuinely nonlinear dispersive K(n, n) equation can be found explicitly.