College of Education for Pure Sciences, University of Basrah discussed a Ph.D. thesis on the nonlinear Ritz approximation for some nonlinear differential equations using the developed Libanov-Schmidt method by the postgraduate student, Mrs. Hadeel Ghazi Abd Ali.

The thesis highlighted the analysis of the nonlinear Ritz approximation for some nonlinear differential equations with boundary conditions using the developed Libanov-Schmidt method.

The thesis aimed at finding the nonlinear Ritz approximation of the Fred Holm function defined by nonlinear homogeneous differential equations such as the Kamassa Holm equation and the Benjamin Bona Mahoney equation, as well as finding the caustic (bifurcation group) and discussing the bifurcation of critical points into key functions.

The thesis concluded that the derivation of the function plane curves and drawing them in the parameter space and revealing the lines related to the field of the Kamassa-Holm equation and the Benjamin-Buna-Mahoney equations via using a program of Mathematica.