In this paper, we study the nonlinear dispersive K(m,n) equations which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the homotopy analysis method in K(m,n) equations. The nonlinear equations K(m,n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m,n) equations are established.
Yıldırım, Ahmet; Ünlü, Canan; and Mohyud-Din, Syed T.
Exact solitary-wave Special Solutions for the Nonlinear Dispersive K(m,n) Equations by Means of the Homotopy Analysis Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 5,
3, Article 7.
Available at: https://digitalcommons.pvamu.edu/aam/vol5/iss3/7