dc.contributor.advisor Tanoğlu, Gamze en dc.contributor.author Güçoğlu, Deniz Hasan en dc.date.accessioned 2014-07-22T13:51:16Z dc.date.available 2014-07-22T13:51:16Z dc.date.issued 2005 en dc.identifier.uri http://hdl.handle.net/11147/3302 dc.description Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2005 en dc.description Includes bibliographical references (leaves: 45-47) en dc.description Text in English; Abstract: Turkish and English en dc.description ix,60 leaves en dc.description.abstract The Hirota Bilinear Method is applied to construct exact analytical one solitary wave solutions of some class of nonlinear differential equations. first one the system of multidimensional nonlinear wave equation with the reaction part in form of the third order polynomial determined by three distinct constant vectors. Second one is the mixed diffusion wave equation in one dimension. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows us reduce the cubic nonlinearity to a quadratic one. In our approach, the velocity of solitary wave is xed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Furthermore, Hirota Bilinear Method is also proposed to solve Brusselator reaction model. The simulations of solutions are illustrated for diffusion wave equation in one dimension. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows us reduce the cubic nonlinearity to a quadratic one. In our approach, the velocity of solitary wave is xed by truncating the Hirota perturbation expansion and it is found in terms of all three roots.Furthermore, Hirota Bilinear Method is also proposed to solve Brusselator reaction model.The simulations of solutions are illustrated for different polynomial roots and parameters as well. en dc.language.iso eng en dc.publisher Izmir Institute of Technology en dc.rights info:eu-repo/semantics/openAccess en_US dc.subject.lcc QA372 .G92 2005 en dc.subject.lcsh Differential equations, Nonlinear en dc.title Exact solution of some nonlinear differential equations by Hirota method en dc.type masterThesis en dc.contributor.department Izmir Institute of Technology. Mathematics en dc.relation.publicationcategory Tez en_US
﻿