M.Phil / MS
Permanent URI for this collectionhttps://repository.cuilahore.edu.pk/handle/123456789/52
This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.
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Item Application of CDSPM and Qualitative Analysis for Dynamical Models(Library Information Services COMSATS University Lahore Campus, 2024-03-17) Sana Shabbir; FA22-RMT-033; Dr. Syed Tahir Raza Rizvi; LHR TP 9353In order to understand nonlinear partial differential equations (NLPDEs), physicists and mathematicians need to study exact solutions. Many analytical methods have been pro posed to acquire solutions for NLPDEs such as Korteweg de Vries equation (KdV), Sin Gordon equation, nonlinear Schrodinger equation (NLSE), and all these equations possess ¨ solitons solutions. A soliton, which arises as a result of dispersion and nonlinearity, is a wave that retain their original features while propagating from one medium to another. The Complete Discrimination System for Polynomial Methods (CDSPM) is a collection of explicit expressions developed with the coefficients of a polynomial that contains real or symbolic variables. Liu was the first who suggested CDSPM technique. Using this method CDSPM we find both the exact, solitary wave (SW) solutions and sensitivity of nonlinear equation. Additionally, in a mathematical framework, sensitivity analysis examines to see how modifications to a system’s parameters affect its behavior. This thesis examines the complex wave patterns of the Gerjikov-Ivanov equation (GIE), commonly known as the derivative nonlinear Schrodinger equation (DNLSE) and analyt- ¨ ical solitons solutions for the cubic-quintic time-fractional nonlinear non-paraxial pulse transmission model. These modifiable model are significant because they are applied in fiber optics communication, nonlinear optics, and optical processing of signals. By using CDSPM approach we explore several solutions, such as rational, SW, and Jacobi elliptic function (JEF). The CDSPM technique is utilized to examine quasi-periodic behavior, bi furcation behavior, critical solution conditions and sensitivity analysis. We also explores the sensitivity analysis and quasi periodic behaviour of our governing models at various initial values. In addition, a number of methods for detecting quasi periodic behaviour will be addressed, including 3D and 2D graphs, time series, and Poincare mapsItem Applications of Variational Integrators and Solitons Solutions for Evaluation Equations(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Sana Ghafoor; FA22-RMT-006; LHR TP 9343; Dr. Syed Tahir Raza Rizvin extensive variety of fields, including biology, chemistry, physics, fiber optics, mechan ics, atmospheric science, and electronics science, use nonlinear partial differential equa tions (NLPDEs), which makes them important. NLPDEs of a particular type are the non linear Schrodinger equations (NLSE). Every NLPDE that is integrable and nonlinear has ¨ a soliton solution. A specific type of solitary wave defined as a soliton has the ability to maintain its original structure even after interacting with another soliton. They are special wave packets which have the capacity to travel long distances without suffering any dis tortion. Solitons are often used in communication due to they are able to transmit signals with no errors throughout long distances and contain an abundance of data. In general, A nonlinear partial differential equation can be resolved to generate a soliton in many appli cations. Variational Integrators (VIs) is a numerical technique in which Lagrangian of the system is used in the action integral. VIs discretized the Lagrangian to obtain a discrete Euler Lagrange equation with the help of the Hamiltonian principle of stationary action. VIs are renowned for their capacity to preserve a distinct multi-symplectic structure while demonstrating desirable long-term energy characteristics. Finite-difference scheme (FDS) are a class of numerical techniques utilized by numerical analysis that approximate deriva tives by employing finite differences in order to solve differential equations (DE). During the past two decades, research on nonlinear models has frequently focused on soliton, a vital description in the NLSE analysis. In particular, the establishment of optical solitons has given rise to a theoretical basis for nonlinear optics. In this thesis, Our objective is to study the nonlinear Klein-Gordon model (NLKGM) and the Stochastic Biswas-Milovic equation (SBME) with parabolic law nonlinearity using the VIs by the use of projection technique, forward, backward, and central difference schemes and the Sub-OdE method. Utilizing the projection technique, we study the VIs of our gov erning model, NLKGM; Additionally, we investigate some of the numerical solutions by ix the use of central difference, forward, and backward techniques. The Sub-OdE approach is also utilized to obtain soliton solutions, that include avariety of solutions:three positive solitons, three Jacobian elliptic function solutions(JEFS), bright solitons, dark solitons, pe riodic solitons, rational solitons, and hyperbolic function solutions. Bose-Einstein conden sation, fiber optic sensors, plasma physics, optical communication, and other fields belong to the applications for these solitons.Item Study of Multiple Solitons and Nonlinear Waves(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Saria Khizar; FA22-RMT-055; Dr. Syed Tahir Raza Rizvi; LHR TP 9345Soliton theory is a significant topic in mathematical physics and applied mathematics with its rapid development since the 1960s. Solitons, also known as SWs, are found in the solutions of many kinds of nonlinear evolution equation (NLEE) or nonlinear partial dif ferential equations (NLPDEs). They have several unique properties and can be used to explaina number of significant physical phenomena. A soliton is a distinct type of SW that possesses the unique characteristic of maintaining its shape and velocity unchanged across collisions. The balance between the nonlinear effects and dispersion leads to a soliton so lution. Solitons are used widely in both pure and applied mathematics, particularly in areas such as differential equations, algebraic and differential geometry, Lie groups, and Lie al gebras. The SIR (Susceptible-Infected-Removed) model is a simple mathematical model of epi demic outbreaks. The present thesis surveys new analytical results about the SIR model. The SIR model is one of the most basic models for describing the temporal dynamics of an infectious disease in a population. It compartmentalizes population into one of three categories: those who are Susceptible to the disease, those who are currently Infectious, and those who have Recovered (with immunity). At its most basic level, the SIR model is a set of ODEs that describes the number (or proportion) of people in each compartment over time. This thesis will analyze the SIR model and provide some solutions through the use of exponential, hyperbolic, and trigonometric functions. Our goal in this work is to find lump soliton solution (LS), rogue wave solution (RW), lump with one kink (LSK), peri odic waves solution (PW), interaction solution between lump, periodic and one kink as well as interaction solution between lump, periodic and two kink soliton wave for different types of NLPDEs. Additionally, M type interaction with periodic, M type rational soliton wave solution, periodic cross kink wave solution, breather wave, homoclinic breather wave, Kuznetsov Ma breathers, W shaped soliton, mixed type solutions will be obtained.