Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematical

This thesis is composed of two parts, namely I and II which are devoted to study the dynamics of inhomogeneous DNA and to the formation of nonliear waves and controlling waves propagation respectively. Also, In part II the different geometric structures are investigated. The part-I is devoted to the study of the dynamics of inhomogeneous DNA. It consists of one chapter, the first one's.with title 2the dynamics of some different inhomogeneous models. The inhomogeneity of the DNA arises when it is exposed to an electric (or electromagnetic) fields or it is subjected to some chemical compounds. That is the structure of DNA is defected. This holds is in cases of interactions with water molecules [1], attachment chemistry of amine-linker molecules [2] and replacing one adenine with 2- aminopurine (2Ap) [3], etc{u2026}) which leads to different chemical structure of DNA nucleotides compounded such as coding, terminator, promoters, etc. [4, 5, 6]. Thus the distribution of DNA polynucleotide chains is inhomogeneous. The different models for describing the dynamics of homogeneous DNA are extrapolated to study the dynamics of inhomogeneous DNA, but they are taken functions in bases- site dependence. This is the main idea that allow to consider the distribution of bases around their center of mass, inhomogeneous (or site-dependent). Thus the coefficients of the total (kinetic and potential) energy are taken site-dependent. In the literature attention was focused to study the breather behavior of the wave function by adopting some assumptions for simplifying the computations

Issued also as CD