The Analysis of Bifurcation Solutions by Angular Singularities

Hussein K. Kadhim, Mudhir A. Abdul Hussain


This paper studies a nonlinear wave equation’s bifurcation solutions of elastic beams situated on elastic bases with small perturbation by using the local method of Lyapunov-Schmidt. We have found the Key function corresponding to the functional related to this equation. The bifurcation analysis of this function has been investigated by the angular singularities. We have found the parametric equation of the bifurcation set (caustic) with the geometric description of this caustic. Also, the critical points’ bifurcation spreading has been found.


Bifurcation solutions; Angular Singularities; Caustic

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