EXACT-SOLUTIONS OF THE COMPLEX MODIFIED KORTEWEG-DE VRIES EQUATION

Firstly, some similarity reductions of the complex modified Korteweg-d e Vries equation (CMKdV), which arises in the asymptotic interpretatio n of one-dimensional plane-wave propogation in a quadratic micropolar medium are discussed. Although it is not a soliton equation solvable b y inverse scattering transformation, its similarity reductions obtaine d by the use of Lie group methods are of mathematical interest. Second ly, the Painleve analysis developed by Weiss et al for nonlinear parti al differential equations is applied to the CMKdV equation, and the da ta obtained by the truncation technique yield some analytical solution s of the ordinary modified Korteweg-de Vries equation and travelling-w ave solutions of the CMKdV equation which are also solutions of the si milarity reduction obtained by classical Lie group analysis.