The Analysis of Bifurcation Solutions by Angular Singularities

Authors

  • Hussein K. Kadhim Department of Mathematics, Faculty of Education for Pure Sciences, University of Basrah, Basrah
  • Mudhir A. Abdul Hussain Department of Mathematics, Faculty of Education for Pure Sciences, University of Basrah, Basrah

DOI:

https://doi.org/10.26713/cma.v10i4.1250

Keywords:

Bifurcation solutions, Angular Singularities, Caustic

Abstract

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.

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References

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Published

31-12-2019
CITATION

How to Cite

Kadhim, H. K., & Hussain, M. A. A. (2019). The Analysis of Bifurcation Solutions by Angular Singularities. Communications in Mathematics and Applications, 10(4), 733–744. https://doi.org/10.26713/cma.v10i4.1250

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Section

Research Article