Department of Mathematics

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Author: search.filters.author.Dr. Syed Tahir Raza RizviSubject: search.filters.subject.fa18

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    PT-Symmetric and W-Shaped Solitons for Nonlinear Schrödinger Equations
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ujala Safdar; FA18-RMT-035; LHR TP 6548; Dr. Syed Tahir Raza Rizvi
    Solitons are the special types of solitary waves who does not change their speed and shape during propagation. When a light pulse in space or time travels in some host medium, it does not dispersive or diffract is called optical Solitons. Optical solitons are produced due to interaction between group velocity dispersion and self-phase modulation. In this thesis, we studied the different forms of optical solitons in non-Kerr law media, parabolic, power, quadratic-cubic and anti-cubic laws with parity-time (PT) symmetric nonlinear and linear lattices. We obtain various types of soliton solutions with the as sistance of the inverse engineering scheme (IES). Under diverse physical conditions, we produce bright, dark and singular solitons. We will also obtained the dynamical behaviour of W-shaped soliton in cigar-shaped Bose Einstein condensate (BEC) in various nonlinear ities
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    Lump and Interaction Solution for the Nonlinear Schrödinger Equation
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Iram Javed; FA18-RMT-075; LHR TP 6550; Dr. Syed Tahir Raza Rizvi
    Solitons are the special types of solitary waves which do not vary their shape and frequency during propagation speed and is also an attractive area of current research in nonlinear physics and mathematics as well as in fiber optics and communication technologies. There are many forms of solitons such as singular soliton, bright soliton, dark soliton and lump soliton. In this thesis, we acquire lumpsolitonsolutionsfor paraxial nonlinear Schr¨odinger equation (NLSE) with the aid of Hirota bilinear method (HBM). In space, lump soliton solutions are rationally positioned in every direction. We also get optical dromions for paraxial NLSE by using modified extended Tanh method. We get domain walls, singular dromions and combined dark-singular dromions. We also list the constraint conditions