On the Variational Approach for Analyzing the Stability of Solutions of Evolution Equations
- Citation:
- Abdel-Gawad, H. I., and M. S. Osman, "On the Variational Approach for Analyzing the Stability of Solutions of Evolution Equations", KYUNGPOOK Math. J., vol. 83, pp. 661-680, 2013.
Abstract:
KYUNGPOOK Math. J.The eigenvalue problems arise in the analysis of stability of traveling waves or rest state solutions are currently dealt with, using the Evans function method. In the literature, it had been shown that, use of this method is not straightforward even in very simple examples. Here an extended \variational" method to solve the eigenvalue problem for the higher order di erential equations is suggested. The extended method is matched to the well known variational iteration method. The criteria for validity of the eigenfunctions and eigenvalues obtained is presented. Attention is focused to nd eigenvalue and eigenfunction solutions of the Kuramoto-Slivashinsky and (K[p,q]) equation.