A study of nonlinear dispersive equations with solitary-wave solutions having compact support

With the use of Adomian decomposition method, the prototypical, genuinely nonlinear K(m, n) equation, ut + (um)x + (un)xxx = 0, which exhibits compactons—solitons with finite wavelength—is solved exactly. Two numerical illustrations, K(2, 2) and K(3, 3), are investigated to illustrate the pertinent features of the proposed scheme. The technique is presented in a general way so that it can be used in nonlinear dispersive equations