o:11663 Qualitative behavior and exact travelling nonlinear wave solutions of the KDV equation doctoral dissertation Kvalitativno ponašanje i tačno rešenje nelineare talasne jednačine KDV : doktorska disertacija en Most phenomena in the scientific field and other domains can be described and classified as nonlinear diffusion equation which normally results from natural phenomena that appear in our daily lives such as water waves at the beach caused by wind or tides, the movement of a ship, or by raindrops; the same applies to other physical and mathematical phenomena. In this study, we tried to find a solution to this kind of equations. IN CHAPTER ONE, we gave brief history of the beginning of the study of waves and we talked about some famous scientists who were interested in this field. IN CHAPTER TWO, we highlighted the diversity and classification of equations in terms of: Linear, Non-linear, Dispersive and Non-dispersive. IN CHAPTER THREE, we introduced the Painlevé method and we applied it into the KdV and modified KdV equations, and in addition to that, we were able to find analytic solutions for these equations. IN CHAPTERS FOUR AND FIVE, we showed several methods of scheme difference, we focused our study on the non-linear term of the KdV equation. IN CHAPTER SIX, we gave some examples of the scheme difference methods and we applied them by Matlab programs. Moreover, our work is supported by pictures and figures. CHAPTER SEVEN shows the future works, we enhanced the work by Appendix. Matemathics - Matematika Datum odbrane: 17. 11. 2015. water waves, KdV equations,analytic solutions yes 47609103 91552101 3261 91552100 47609103 2016-07-14T12:36:55.053Z 45 no 46 mentor Attia. Mostafa 2015 63 mentor Miodrag, 1949- Mateljević 2015 63 član komisije Miljan, 1973- Knežević 2015 63 član komisije Miloš, 1962- Arsenović 2015 63 član komisije Božidar, 1969- Jovanović 2015 VII, 109 listova 3337981 http://phaidrabg.bg.ac.rs/o:11663 no yes 1 2016-07-14T12:36:55.320Z 70 11 1066609 1066646 11 1066609 1066634 11 1066732 1066743 1066746 water waves, KdV equations,analytic solutions 1738 11A31 2015