dc.contributor.author Nayeri, HamidReza dc.date.accessioned 2019-10-09T18:22:42Z dc.date.available 2019-10-09T18:22:42Z dc.identifier.uri http://hdl.handle.net/10464/14539 dc.description.abstract In presenting this thesis, we try to find all non-periodic travelling waves of the generalized Korteweg-de Vries (gKdV) equation en_US u_t +\alpha u^p u_x +\beta u_{xxx}=0 using an energy analysis method. Since the power p in the gKdV equation is arbitrary, we consider positive integer values for $p$. We first check the method for two cases where p=1 and p=2 which are known as the KdV and the mKdV equations, respectively. Then, we look at the general case where p greater than or equal 3 is arbitrary. By applying the energy analysis method on the KdV and the mKdV equations, we will find an explicit form of solitary waves on a non-zero background. Afterwards, we reparametrize the derived solutions in terms of speed and the background size to interpret these solutions physically. We also look at some limiting cases in which heavy-tailed and kink waves arise in the mKdV equation. At last, we split up the gKdV equation into two cases of odd and even $p$ powers and apply a similar derivation. In each case, the implicit solutions are introduced and characterized by their features. dc.language.iso eng en_US dc.publisher Brock University en_US dc.subject Solitary wave on a background en_US dc.subject Heavy-tail wave en_US dc.subject Kink wave en_US dc.subject gKdV equation en_US dc.title Travelling Wave Solutions on a Non-zero Background for the Generalized Korteweg-de Vries Equation en_US dc.type Electronic Thesis or Dissertation en_US dc.degree.name M.Sc. Physics en_US dc.degree.level Masters en_US dc.contributor.department Department of Physics en_US dc.degree.discipline Faculty of Mathematics and Science en_US refterms.dateFOA 2021-08-05T01:32:29Z
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