Abstract
A system of equations u t +( u 2 /2-α u m x +β u n x ) x =0 ( m , n : positive integers, β≠0) is studied by means of Hirota's method and the singular manifold expansion. The singular manifold expansion yields the transformation of the system into bilinear forms or higher order ones and we obtain some explicit solutions of the system in physically interesting but non-integrable cases.
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