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New Compacton Solutions and Solitary Pattern Solutions for Modified Nonlinearly Dispersive mK (m,n,a,b) Equation

In this paper exact solutions of a new modified nonlinearly dispersive equation (simply called mK(m, n, a, b) equation), um–1ut + α(un)x + β(ua(ub)xx)x = 0, is investigated by using some direct algorithms. As a result, abundant new compacton solutions (solitons with the absence of infinite wings) and solitary pattern solutions (having infinite slopes or cusps) are obtained.