Adil Jhangeer

Bio: Adil Jhangeer is an academic researcher from Namal College. The author has contributed to research in topics: Nonlinear system & Conservation law. The author has an hindex of 13, co-authored 70 publications receiving 499 citations. Previous affiliations of Adil Jhangeer include Qassim University & National University of Computer and Emerging Sciences.

Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method

Abstract: The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. In this article, the sine-Gordon expansion (SGE) approach and the generalized Kudryashov (GK) scheme are used to establish broad-spectral solutions including unknown parameters and typical analytical solutions are recovered as a special case. The well-known bell-shape soliton, kink, singular kink, compacton, contracted bell-shape soliton, periodic soliton, anti-bell shape soliton, and other shape solitons are retrieved for the definite value of these constraints. The 3D and contour plots of some of the results obtained are sketched by assigning individual values of the parameter and analyzed the dynamical behavior of the waves. Furthermore, the compatibility of the two approaches has been compared and examined the efficiency to ascertain soliton solutions.

Nonlinear dispersion in parabolic law medium and its optical solitons

Abstract: This paper studies the optical soliton solutions of a nonlinear Schrodinger equation (NLSE) involving parabolic law of nonlinearity with the presence of nonlinear dispersion by using the generalized auxiliary equation technique. As a result, new varieties of exact traveling wave solutions have been uncovered, comprising of the hyperbolic trigonometric, trigonometric, exponential, and rational. Interestingly, we obtain the bright, dark, periodic, singular, and other soliton solutions to the nonlinear model. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behaviour. Furthermore, the findings discussed in this present investigation may be useful in explaining the propagation of optical solitons in a weakly nonlocal parabolic law medium.

Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation

Abstract: In this paper, the nonlinear modified Gardner (mG) equation is under consideration which represents the super nonlinear proliferation of the ion-acoustic waves and quantum electron-positronion magneto plasmas. The considered model is investigated with the help of Lie group analysis. Lie point symmetries are computed under the invariance criteria of Lie groups and symmetry group for each generator is reported. Furthermore, the one-dimensional optimal system of subalgebras is developed by adjoint technique and then we compute the similarity reductions corresponding to each vector field present in the optimal system, with the help of similarity reduction method we have to convert the PDE into the ODE. Some exact explicit solutions of obtained ordinary differential equations were constructed by the power series technique. With the aid of the Galilean transformation, the model is transformed into a planer dynamical system and the bifurcation behaviour is recorded. All practicable types of phase portraits with regard to the parameters of the problem considered are plotted. Meantime, sensitivity is observed by utilizing sensitivity analysis. In addition, the influence of physical parameters is studied by the application of an extrinsic periodic power. With additional perturbed term, quasi-periodic and quasi-periodic-chaotic behaviours is reported.

Conserved Quantities in $f(R)$ Gravity via Noether Symmetry

Abstract: We investigate f(R) gravity using the Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of f(R) models in the presence of the gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.

New optical solitons of perturbed nonlinear Schrödinger-Hirota equation with spatio-temporal dispersion

Abstract: The perturbed nonlinear Schrodinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated in this study using an improved Sardar sub-equation method. The Kerr and power laws of nonlinearity are taken into account. As a result of this improved technique, many constraint conditions required for the existence of soliton solutions emerge. We retrieved several solutions such as the bright solitons, dark solitons, singular solitons, mixed bright–dark solitons, singular-bright combo solitons, periodic, and other solutions. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.

The Supernova Legacy Survey: Measurement of Omega_m, Omega_l and w from the First Year Data Set

Abstract: We present distance measurements to 71 high redshift type Ia supernovae discovered during the first year of the 5-year Supernova Legacy Survey (SNLS). These events were detected and their multi-color light-curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshift. With this data set, we have built a Hubble diagram extending to z = 1, with all distance measurements involving at least two bands. Systematic uncertainties are evaluated making use of the multiband photometry obtained at CFHT. Cosmological fits to this first year SNLS Hubble diagram give the following results: {Omega}{sub M} = 0.263 {+-} 0.042 (stat) {+-} 0.032 (sys) for a flat {Lambda}CDM model; and w = -1.023 {+-} 0.090 (stat) {+-} 0.054 (sys) for a flat cosmology with constant equation of state w when combined with the constraint from the recent Sloan Digital Sky Survey measurement of baryon acoustic oscillations.

Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)

Abstract: The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form $$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$ , which we solve exactly using a kind of perturbational approach.

Cosmological and Solar System Consequences of f(R,T) Gravity Models

Abstract: To find more deliberate f ( R , T ) cosmological solutions, we take our previous paper further by studying some new aspects of the considered models via investigation of some new cosmological parameters/quantities to attain the most acceptable cosmological results. Our investigations are performed by applying the dynamical system approach. We obtain the cosmological parameters/quantities in terms of some defined dimensionless parameters that are used in constructing the dynamical equations of motion. The investigated parameters/quantities are the evolution of the Hubble parameter and its inverse, the “weight function”; the ratio of the matter density to the dark energy density and its time variation; the deceleration; the jerk and the snap parameters; and the equation-of-state parameter of the dark energy. We numerically examine these quantities for two general models R + α R - n + - T and R log [ α R ] q + - T . All considered models have some inconsistent quantities (with respect to the available observational data), except the model with n = - 0.9 , which has more consistent quantities than the other ones. By considering the ratio of the matter density to the dark energy density, we find that the coincidence problem does not refer to a unique cosmological event; rather, this coincidence also occurred in the early Universe. We also present the cosmological solutions for an interesting model R + c 1 - T in the nonflat Friedmann–Lemaitre–Robertson–Walker metric. We show that this model has an attractor solution for the late times, though with w ( DE ) = - 1 / 2 . This model indicates that the spatial curvature density parameter gets negligible values until the present era, in which it acquires the values of the order 10 - 4 or 10 - 3 . As the second part of this work, we consider the weak-field limit of f ( R , T ) gravity models outside a spherical mass immersed in the cosmological fluid. We have found that the corresponding field equations depend on the both background values of the Ricci scalar and the background cosmological fluid density. As a result, we attain the parametrized post-Newtonian parameter for f ( R , T ) gravity and show that this theory can admit the experimentally acceptable values of this parameter. As a sample, we present the post-Newtonian gamma parameter for general minimal power law models, in particular, the model R + c 1 - T .

f ( R , T ) cosmological models in phase space

Abstract: We investigate the cosmological solutions of $f(R,T)$ modified theories of gravity for a perfect fluid in a spatially Friedmann-Lema\^{\i}tre-Robertson-Walker metric through the phase-space analysis, where $R$ is the Ricci scalar and $T$ denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze the three general theories with the Lagrangians of minimal $g(R)+h(T)$, pure nonminimal $g(R)h(T)$, and nonminimal $g(R)(1+h(T))$ couplings through the dynamical systems approach. We introduce a few variables and dimensionless parameters to simplify the equations to more concise forms. The conservation of the energy-momentum tensor leads to a constraint equation that, in the minimal gravity, confines the functionality of $h(T)$ to a particular form, and hence relates the dynamical variables. In this case, acceptable cosmological solutions that contain a long enough matter-dominated era followed by a late-time accelerated expansion are found. To support the theoretical results, we also obtain numerical solutions for a few functions of $g(R)$, and the results of the corresponding models confirm the predictions. We separate the solutions into six classes which demonstrate more acceptable solutions and there is more freedom to have the matter-dominated era than in $f(R)$ gravity. In particular, there is a new fixed point which can represent the late-time acceleration. We draw different diagrams of the matter densities (consistent with the present values), the related scale factors, and the effective equation of state. The corresponding diagrams of the parameters illustrate that there is a saddle acceleration era which is a middle era before the final stable-acceleration de Sitter era for some models. All presented diagrams determine radiation, matter, and late-time acceleration eras very well. The pure nonminimal theory suffers from the absence of a standard matter era, though we illustrate that the nonminimal theory can have acceptable cosmological solutions.

Anisotropic compact stars in f(G) gravity

Abstract: This paper is devoted to study the possibility of forming anisotropic compact stars in modified Gauss–Bonnet, namely called as f(G) theory of gravity which is one of the strong candidates, responsible for the accelerated expansion of the universe. For this purpose, we have used analytical solution of Krori and Barua metric to the Einstein field equations with anisotropic form of matter and power law model of f(G) gravity. To determine the unknown constants in Krori and Barua metric, we have used the sample of compact stars, 4U1820-30, Her X-1, SAX J 1808-3658. The physical behavior of these stars have been analyzed with the observational data. In this setting, we have checked all the regularity conditions and stability of the compact stars 4U1820-30, Her X-1, SAX J 1808-3658.