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 Solitary Wave Solutions and Stability nalysis for Nonlinear Evolution Equation(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2024) Asmavia Shahid; SP23-RMT-005; Dr. Syed Tahir Raza Rizvi; LHR TP 9587In order to understand nonlinear partial differential equations (NLPDEs), physicists and mathematicians need to study exact solutions. Many NLPDEs such as Korteweg de Vries equation (KdV), Sin-Gordon equation, nonlinear Schr¨odinger equation (NLSE), and other 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 trial equation method proposed by Liu it is an advanced analyt- ical method for finding the exact solution of NLPDE in the study of solitons. Another method 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. Using this method CDSPM, we find both the quasi periodic behaviour and sensitivity of nonlinear equation. Additionally, in a mathematical framework, sensitiv- ity analysis examines to see how modifications to a system’s parameters affect its behavior. This thesis examines nonlinear Kakutani-Matsuuchi (NKM) model of internal gravity waves. The evolution of lengthy internal gravity waves in a stratified fluid medium is meticulously captured by the (1+1)-dimensional NKM model. By using trial approach we explore several solutions, such as SW, rational and Jacobi elliptic function (JEF). The CDSPM technique is utilized to examine quasi-periodic behavior, critical solution conditions, bifurcation behav- ior and sensitivity analysis. We also explores the quasi periodic behaviour and sensitivity analysis of our governing models at various initial values. Key words: Kakutani-Matsuuchi equation; solitons, complete discriminant system; quali- tative behaviour; quasi periodic behaviour; sensitivity analysis.Item Extraction of Solitons Emerging in Nonlinear Dynamics(Library Information Services COMSATS University Lahore Campus, 2024-03-18) Bismah Yousaf; SP23-RMT-006; Dr. Hafiz Muhammad Afzal Siddiqui; LHR TP 9574The extraction of solitons that emerge in nonlinear dynamics is examined in this thesis, with particular attention to two significant models: the Perturbed Chen-Lee-Liu and the Biswas Milovic models. These models, which are renowned for their complexity in nonlinear wave propagation, describe a wide range of physical phenomena. The Extended Modified Auxil iary Equation Method (EMAEMM), a powerful yet efficient method for resolving nonlinear partial differential equations (NLPDEs), is used to derive solution solutions to these mod els. The EMAEMM method is a useful tool in nonlinear analysis as it makes it easier to find exact solutions by breaking down the equations into simplified forms. The ability of soliton to hold its shape during propagation makes it useful in a variety of applications, including fluid dynamics, optical fibers, and plasma physics. The stability and sensitivity of the resulting solitons is examined, and a number of graphical representations—all gen erated via Mathematica—are shown, including 2D, 3D, density linear, 1D, slice contour plotting, and stream density plots. The observed solitons exhibit a wide variety of behav iors and include bright, dark, kink, periodic, and optical solitons. Insights into the stability and representation of solitons in mathematical physics are provided by this comprehensive examination of soliton dynamics in nonlinear systems.