Işık Üniversitesi Kurumsal Akademik Belleği :: DSpace Angular

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Numerical simulation of blow-up solutions for the generalized Davey-Stewartson system
(Taylor & Francis Ltd, 2011-03) Muslu, Gülçin Mihriye; Erbay, Hüsnü Ata
Blow-up solutions for the generalized Davey-Stewartson system are studied numerically by using a split-step Fourier method. The numerical method has spectral-order accuracy in space and first-order accuracy in time. To evaluate the ability of the split-step Fourier method to detect blow-up, numerical simulations are conducted for several test problems, and the numerical results are compared with the analytical results available in the literature. Good agreement between the numerical and analytical results is observed.
Closing the gap in the purely elliptic generalized Davey-Stewartson system
(Pergamon-Elsevier Science Ltd, 2008-10-15) Eden, Osman Alp; Erbay, Hüsnü Ata; Muslu, Gülçin Mihriye
In this note we improve the results presented previously on global existence and global nonexistence for the Solutions of the purely elliptic generalized Davey-Stewartson system. These results left a gap in the parameter range where neither a global existence result nor a global nonexistence result could be established. Here we are able to show that when the coupling parameter is negative there is no gap. Moreover, in the case where the coupling parameter is positive we reduce the size of the gap.