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Yayın Numerical simulation of blow-up solutions for the generalized Davey-Stewartson system(Taylor & Francis Ltd, 2011-03) Muslu, Gülçin Mihriye; Erbay, Hüsnü AtaBlow-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.Yayın Contribution of higher order terms in nonlinear ion-acoustic waves: strongly dispersive case(Physical Soc Japan, 2002-08) Demiray, HilmiContribution of higher order terms in the perturbation expansion for the strongly dispersive ion-plasma waves is examined through the use of modified reductive perturbation method developed by us [J. Phys. Soc. Jpn. 68 (1999) 1833]. In the analysis it is shown that the lowest order term in the expansion is governed by the nonlinear Schrodinger equation while the second order term is governed by the linear Schrodinger equation. For the small wave number region a set of solution is presented for the evolution equations.Yayın Stability of solitary waves for three-coupled long wave-short wave interaction equations(Oxford Univ Press, 2011-08) Borluk, Handan; Erbay, SaadetIn this paper, we consider a three-component system of 1D long wave-short wave interaction equations. The system has two-parameter family of solitary wave solutions. We prove orbital stability of the solitary wave solutions using variational methods.
