Browsing by Author "Syed Tahir Raza Rizvi"

Now showing 1 - 2 of 2

Exact and Multiple Solitons with Conservation Laws for Nonlinear Schrodinger Equations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Ijaz Ali; FA17-PMT-014; Syed Tahir Raza Rizvi; LHR TP 7733
Asoliton being atraveling wave solution of a nonlinear partial differential equation (NLPDE) has remarkable properties. These wave solutions are stable and have significant role in the mathematical physics particularly in fiber technology. A soliton (dromion) maintains its speed, amplitude as well as shape over large distance in a nonlinear (NL) and non-local media [75]. In the domain of NL optical fibers, the importance of optical dromions is vi tal. They possess a significant potential of becoming information carriers in the field of telecommunication because of their tremendous feature of long propagation without any change in shape and attenuation [46]. These dromions being light pulses are described and governed by nonlinear Schr¨ odinger equation (NLSE). Optical solitons are the solutions of NLSEs and they can be evaluated by utilizing different kinds of nonlinearities. A NLSE is a classical field equation whose major applications involve the transmission of light in NL optical fibers and planar waveguides [5]. In the areas of engineering and applied sciences, numerous NLSEs exhibit conservation of energy, mass and momentum as well as electric charges. The presence of an infinite num ber of conservation laws (CLs) of a NLSE assures the complete integrability of the NLSE [52]. In this thesis, we obtain CLs for various NLSEs like modulated compressional disper sive Alfv´en (MCDA) model [57], Heisenberg ferromagnetic spin chains equation (HFSCE) [56], Biswas-Arshed model (BAM) [58], perturbed Radhakrishnan-Kundu-Lakshmanan (PRKL) model [19], Chen-Lee-Liu equation (CLLE) [24] and some other NLSEs. For the investigation of solvability of NLSEs, we have a very impressive technique known as the Painlev´e test (P-test) [16]. This tremendous test was firstly initiated for the analysis of the singularities structure for ordinary differential equations (ODEs). In this dissertation, we investigate the integrability by means of P-test for above mentioned NLSEs. At the end, we study different kinds of soliton solutions of numerous NLSEs by means of x Bernoulli’s equation approach (BEA) [74], sine-cosine method (SCM) [74], unified method (UM) [1], Hirota bilinear method (HBM) [105] and sub-ODE approach [114]. We analyse optical soliton solutions for above mentioned models and some other NLSEs. We also investigate optical dromions for Parity-Time symmetry (PTS) lattices with quadratic and anti cubic nonlinearities of the propagation equation [35]. Over and above board, we obtain multiple solitons for PRKL model and discuss one soliton transformation, two and three soliton interactions using HBM.
Group H-magic labelings of graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2015) Syed Tahir Raza Rizvi; FA11-PMT-002; Dr. Kashif Ali; LHR TP 5283
A simple graph G admits an H-covering if each edge in E G is a member of a sub- graph of G isomorphic to H. An H-magic labeling of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph G onto the set 1 2 V G E G if there occurs a positive integer , called the magic sum, such that for every subgraph H of G isomorphic to H, the sum wt H v V H v e E H e is equal to . The sum wt H is termed as, the H-weight. A graph is called H-magic (H-supermagic) if it possesses an H-magic (H-supermagic) labeling. If H is isomorphic to K2, then resulting labeling is known as edge-magic total labeling. This dissertation studies about the formulation of cycle-supermagic labelings for the disjoint union of isomorphic and non isomorphic copies of different families of graphs. We also evaluate the K2-supermagic labelings of some families of alpha trees. More- over, we ﬁnd the cycle-(super)magic labelings of uniform subdivided graph and cycle- supermagic labelings for non uniform subdivisions of fans and triangular ladders graphs. We also articulate about the introduction of H-groupmagic total labeling of a graph G over a ﬁnite abelian group A . In this study, we determine the H-groupmagic total labelings of fan graphs and disjoint union of isomorphic as well as non-isomorphic copies of fan graphs over ﬁnite abelian group A 3 n, where n 3