Compacton solutions for a class of two parameter generalized odd-order Korteweg-de Vries equations

We study the fifth-order fully nonlinear K(m,n,p) equations and obtain a class of exact compacton solutions. We find that addition of the fifth-order dispersion term increases the range of the nonlinear parameters m, n, and p for which these compacton solutions are allowed. We consider the Hamiltonian structure and conservation laws of this class of equations. We also study the class of two parameter generalized odd-order equations and obtain the exact compacton solutions and the range of the nonlinearity and dispersion parameters as well as the relation between them.