The College of Education for Pure Sciences, Department of Mathematics, University of Basra, discussed a master’s thesis on branching solutions of the fourth-order nonlinear differential equation using the local method of Libanov-Schmidt in three dimensions.
The message submitted by the student (Zahra Abdullah Shawi) included
Studying the branching solutions of the nonlinear ordinary differential equation, using the local reduction method of Libanov-Schmidt, where we presented in this study two examples. Algebraic equations, we also found the branching diagram of the corresponding branching equation, which includes the number of solutions and their distribution in the parameter space, and we found the geometric drawing of the characteristic group and the number of solutions, and we considered the real solutions as solutions for a dynamic system, after that we found the points in the phase portrait (phase space) corresponding to them for each region from the parameter space.
In the case of the second example, we also studied a non-linear fourth-order heterogeneous differential equation, where we extracted the branching equation for it using the local method of Libanov-Schmidt, we got three nonlinear algebraic equations, we also found the branching scheme of the corresponding branching equation
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