Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Scopus Q: search.filters.scopusQuartile.Q1Subject: search.filters.subject.First integral method

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  • Article
    Citation - WoS: 17
    Citation - Scopus: 25
    The First Integral Method for Constructing Exact and Explicit Solutions To Nonlinear Evolution Equations
    (John Wiley and Sons Inc., 2012) Aslan, İsmail
    Problems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so-called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 34
    Exact and Explicit Solutions To Nonlinear Evolution Equations Using the Division Theorem
    (Elsevier Ltd., 2011) Aslan, İsmail
    In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a parameter condition. Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived in a concise manner.