Browsing by Subject "Exact solutions"

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    The Hirota direct method
    (2005) Pekcan, Aslı
    The search for integrability of nonlinear partial differential and difference equations includes the study on multi-soliton solutions. One of the most famous method to construct multi-soliton solutions is the Hirota direct method. In this thesis, we explain this method in detail and apply it to explicit examples.
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    Solutions of the extended Kadomtsev-Petviashvili-Boussinesq equation by the Hirota direct method
    (Taylor & Francis Asia Pacific (Singapore), 2009) Pekcan, A.
    We show that we can apply the Hirota direct method to some non-integrable equations. For this purpose, we consider the extended Kadomtsev-Petviashvili- Boussinesq (eKPBo) equation with M variable which is (uxxx-6uu x)x + a11uxx + 2ΣMk=2 a1kuxk + ΣMi,j=2aijuxixj=0, where aij = a ji are constants and xi = (x, t, y, z,⋯,x M). We will give the results for M = 3 and a detailed work on this equation for M = 4. Then we will generalize the results for any integer M > 4. © 2009 The Author(s).
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    Some further properties of the accelerated Kerr-Schild metrics
    (2004) Gürses, M.; Sarıoǧlu, Ö.
    We extend the previously found accelerated Kerr-Schild metrics for Einstein-Maxwell-null dust and Einstein-Born-Infeld-null dust equations to the cases including the cosmological constant. This way we obtain the generalization of the charged de Sitter metrics in static space-times. We also give a generalization of the zero acceleration limit of our previous Einstein-Maxwell and Einstein-Born-Infeld solutions.