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This book deals with wide range of applications of continuous symmetry groups to some physically important systems which are: the coupled Klein-Gordon-Schrodinger equation with its generalized form, the Dullin-Gottwald-Holm Equation, the Generalized Bretherton equation with variable coefficients. For all the three different equations, we have derived some special type of solutions including traveling wave solutions, periodic solutions, kink wave solutions, solitons etc. and we have plotted some figures also to see the propogation and asymptotic behaviour of all types of waves.