Department of Mathematics

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    New Solitary Wave Solution for Nonlinear Schrodinger Equation
    (COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2020) Urooj Akram,; FA16-RMT-005; Dr. Syed Tahir Raza Rizvi, Assistant Profesor; lhr tp 5179
    A nonsingular and localized wave which propagates without change of velocity and shape is called a solitary wave. A soliton is a solution of NLPDE which has a per manent form and is localized. A solitary traveling wave does not obey superposition principle; it does not disperse. Solitary waves retain its permanent structure even when it collides with other soliton [25]. Soliton has many applications in other fields like engineering and biology. Soliton solutions can be calculated with the help of differ ent nonlinearities. These nonlinearities are Kerr law, power law, parabolic law, dual power law, exponential law etc. In this thesis we will study, the soliton solutions of Lakshmanan-Porsezian-Danial (LPD) model. In order to obtain exact soliton solutions several powerful methods have been proposed. We will use modified trail equation method with Kerr and parabolic law to obtain some hyperbolic and rational function solutions to LPD model. We also find new and more general exact traveling wave solution by using improved G′/G-expansion method with Kerr and parabolic laws of nonlinearities
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    Cosmological Evolution in the Background of Non-Minimally Coupled Gravity
    (COMSATS University Islamabad, Lahore Campus Library Information Services, CUI Lahore, 2020) Muhammad Zeeshan,; FA16-RMT-010; DR. MUHAMMAD ZUBAIR, Assistant Profesor [Supervisor]; lhr tp 5182
    In current cosmic scenario, an accelerated expansion era is being reported by various observations. The reasoning of such scenario is still unknown, the pres ence of an unknown energy component is seen which is named as DE. There are various approaches to discuss the existence of DE and present acceleration of universe. One of such attempts is the modification of Einstein’s gravity, here we attempt to explore this problem within the modified gravity based on non minimal matter-geometry coupling. We examine f(R,T,Q) theory (where R is the Ricci Scalar, T is the trace of EMT Tuv and Q = RuvTuv is interaction of EMT Tµν and Ricci Tensor Ruv). We formulate the dynamical equations in the back ground of FLRW model and find the result of non-conserved EMT using the divergence of the field equations. In this scenario test particles deviates from geodesic motion and an extra force is there due to non-minimal coupling. We appliedthis result to findanexpressionforenergydensityρforparticularchoice of Lagrangian. Furthermore, we discuss the energy bound on the modelparam eters and discuss the late time cosmic acceleration for best suitable parameters in accordance with recent observations.
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    Discrete Mathematical Analysis Of Vascular Tumor
    (Library Information Services, COMSATS University, Lahore Campus, 2020) Muhammad Awais,; FA16-RMT-007; Dr. Ayesha Sohail, Assistant Profesor [Supervisor]; LHR TP 5181
    In this thesis, the growing field of mathematical oncology is discussed in a discrete manner. The discrete mathematical modeling of cancer has remained a topic of debate during the past decade. In the proposed research, we aim to discuss the effects of chemotherapy, on angiogenesis and on the associated tumour microenvironment with the help of a computational tool. Different combination of drug applications will be analyzed in order to predict the best dose candidate to eliminate the tumour. During this research, we will demonstrate, with the help of mathematical tools, the importance discrete agent based approach to model cancer invasion.