The College of Education for Pure Sciences, Department of Mathematics, University of Basra, discussed a master’s thesis on incomplete branching solutions of some nonlinear differential equations using the local method of Libanov-Schmidt.
The message presented by the student (Abbas Fadel Abbas Saleh) included
Study of incomplete branching solutions of some nonlinear differential equations, using the local reduction method of Libanov-Schmidt, where we presented in this study two examples. It appeared as a non-linear system of two algebraic equations, we also found the branching diagram of the corresponding incomplete branching equation, which includes the number of solutions and their distribution in the parameter space, and we found the geometric diagram of the characteristic set and the number of solutions, and we considered the real solutions as solutions for a dynamic system, after that we found the points in phase portrait ( phase space) corresponding to each region of the parameter space.
In the case of the second example, we also studied the nonlinear Predator-Bry differential equation of the second order inhomogeneous in the case of symmetry, where we extracted the incomplete branching equation for it using the local method of Libanov-Schmidt, we obtained a nonlinear system of two algebraic equations, we also found the incomplete branching scheme for the corresponding branching equation