Analytical solutions to a quasilinear differential equation related to the Lane–Emden equation of the second kind

We apply the δ-expansion method to a transformed Lane–Emden equation. The results are then transformed back, and we recover analytical solutions to the Lane–Emden equation of the second kind (which describes Bonnor–Ebert gas spheres) in a special case. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations, as we see when we compare the obtained analytical solutions to numerical results.     

Bandlimited implicit Runge–Kutta integration for Astrodynamics

We describe a new method for numerical integration, dubbed bandlimited collocation implicit Runge–Kutta (BLC-IRK), and compare its efficiency in propagating orbits to existing techniques commonly used in Astrodynamics. The BLC-IRK scheme uses generalized Gaussian quadratures for bandlimited functions. This new method allows us to use significantly fewer force function evaluations than explicit Runge–Kutta schemes. In particular, we use a low-fidelity force model for most of the iterations, thus minimizing the number of high-fidelity force model evaluations. We also investigate the dense output capability of the new scheme, quantifying its accuracy for Earth orbits. We demonstrate that this numerical integration technique is faster than explicit methods of Dormand and Prince 5(4) and 8(7), Runge–Kutta–Fehlberg 7(8), and approaches the efficiency of the 8th-order Gauss–Jackson multistep method. We anticipate a significant acceleration of the scheme in a multiprocessor environment.     

Approximate analytic solutions to the isothermal Lane–Emden equation

We derive accurate analytic approximations to the solution of the isothermal Lane–Emden equation, a basic equation in Astrophysics that describes the Newtonian equilibrium structure of self-gravitating, isothermal fluid spheres. The solutions we obtain, using analytic arguments and rational approximations, have simple forms, and are accurate over a radial extent that is much larger than that covered by conventional series expansions around the origin. Our best approximation has a maximum error on density of 0.04 % at 10 core radii, and is still within 1 % from an accurate numerical solution at a radius three times larger.     

Nonlinear ion acoustic waveforms for Kadomstev–Petviashvili equation

The reductive perturbation method has been employed to derive the Kadomstev–Petviashvili equation for small but finite amplitude electrostatic ion-acoustic waves. An algebraic method with computerized symbolic computation is applied in obtaining a series of solutions of the Kadomstev–Petviashvili equation. Numerical studies have been made using plasma parameters reveals different waveforms such as bell-shaped solitary pulses, rational pulses and others with singularity at finite points which called blowup solutions in addition to the propagation of explosive pulses. The result of the present investigation may be applicable to some plasma environments, such as ionosphere plasma.     

Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites.     

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves with electrons featuring non-extensive distribution

Cylindrical Zakharov–Kuznestov equation for ion-acoustic waves comprising of ions and electrons featuring non-extensive distribution are derived from the fluid equations through reductive perturbation technique. System of first order ordinary differential equations is obtained from Zakharov–Kuznestov equation through dynamical system approach and ultimately it is solved using numerical method. It is found that the electron to positron ratio parameter and the non-extensive distributed parameter due to electron play crucial role on the solution.     

Kadomtsev–Petviashvili equation for solitary waves in warm dense astrophysical electron-positron-ion plasmas

Theoretical investigation is carried out to understand the dynamics and stability of three dimensional ion solitary waves propagating in dense plasma comprising of ultra-relativistic degenerate electrons and positrons and warm ions. A linear dispersion relation is derived which shows a strong dependence of wave on positron concentration (through the change of density balance) and ion-to-degenerate electron temperature ratio. A nonlinear Kadomtsev-Petviashvili equation is derived by employing the reductive perturbation technique and solved analytically and the conditions for existence of stable solitary waves are found. The analysis reveals that only compressive solitary waves exist in the system. Effects of the change of density balance and Fermi temperature ratios are studied in detail, both analytically and numerically. Furthermore, the conditions for stable solitary waves are discussed by using energy consideration method. The numerical results are also presented by using the parameters consistent with the degenerate and ultrarelativistic astrophysical plasmas.     

An elegant perturbation solution for the Lane–Emden equation of the second kind

Perturbation solutions are obtained for the Lane–Emden equation of the second kind which describe Bonnor–Ebert gas spheres. In particular, we employ the field-theoretic perturbative procedure due to Bender et al. to obtain analytical solutions to the nonlinear initial value problem. We find that the method allows one to construct perturbation solutions which converge rapidly to the true solutions in many cases, as it allows one to more accurately represent the influence of nonlinear terms in the linearized equations. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations.     

A new technique for understanding magnetosphere–ionosphere coupling using directional derivatives of SuperDARN convection flow

The purpose of this paper is to present and evaluate a new technique to better understand ionospheric convection and it’s magnetospheric drivers using convection maps derived from the Super Dual Auroral Radar Network (SuperDARN). We postulate that the directional derivative of the SuperDARN ionospheric convection flow can be used as a technique for understanding solar wind–magnetosphere–ionosphere coupling by identifying regions of strong acceleration/deceleration of plasma flow associated with drivers of magnetospheric convection such as magnetic reconnection. Thus, the technique may be used to identify the open–closed magnetic field line boundary (OCB) in certain circumstances. In this study, directional derivatives of the SuperDARN ionospheric convection flow over a four and a half hour interval on Nov. 04, 2001, is presented during which the interplanetary magnetic field was predominantly southward. At each one-minute time point in the interval the positive peak in the directional derivative of flow is identified and evaluated via comparison with known indicators of the OCB including the poleward boundary of ultraviolet emissions from three FUV detectors onboard the IMAGE spacecraft as well as the SuperDARN spectral widths. Good comparison is found between the location of the peak in the directional derivative of SuperDARN flow and the poleward boundary of ultraviolet emissions confirming that acceleration of ionospheric plasma flow is associated with magnetic reconnection and the open–closed boundary.     

Gravitational wave radiation from a double white dwarf system inside our galaxy： a potential method for seeking strange dwarfs

Like the investigation of double white dwarf （DWD） systems, strange dwarf （SD） - white dwarf （WD） system evolution in Laser Interferometer Space Antenna （LISA）＇s absolute amplitude-frequency diagram is investigated. Since there is a strange quark core inside an SD, SDs＇ radii are significantly smaller than the value predicted by the standard WD model, which may strongly affect the gravitational wave （GW） signal in the mass-transferring phases of binary systems. We study how an SD-WD binary evolves across LISA＇s absolute amplitude-frequency diagram. In principle, we provide an executable way to detect SDs in the Galaxy＇s DWD systems by radically new windows offered by GW detectors.     

Higher dimensional exact solutions for a charged fluid sphere in general theory of relativity

The exact higher dimensional solutions of Einstein-Maxwell field equations for spherically symmetric distribution of charged perfect fluid are obtained by using the method originally used by Hajj-Boutros and Sfeila (Gen. Relativ. Gravit. 18(4):395, 1986) for four-dimensional space-time. The new exact solutions have been generated from those of Khadekar et al. (J. Indian Math. Soc. 68(1–4):33, 2001), Humi and Mansour (Phys. Rev. D 29(6):1076, 1984) and Banerjee and Santos (J. Math. Phys. 22(4):824, 1981) in the frame work of higher dimensional space-time. The various physical properties are also discussed.     

Solitary solution and energy for the Kadomstev–Petviashvili equation in two temperatures charged dusty grains

The nonlinear properties of small amplitude dust-acoustic solitary waves (DAWs) in a homogeneous unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili (KP) equation. The effects of the presence of charged hot and cold dust grains on the nature of DAWs were discussed. Moreover, the energy of two temperatures charged dusty grains were computed. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments.     

Asymmetric periodic solutions of the averaged Hill problem with allowance for a planet’s oblateness

We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.     

CoRoT-2a Magnetic Activity: Hints for Possible Star–Planet Interaction

CoRoT-2a is a young (≈0.5 Gyr) G7V star accompanied by a transiting hot-Jupiter, discovered by the CoRoT satellite (Alonso et al. Astron Astrophys 482:L21, 2008; Bouchy et al. Astron Astrophys 482:L25, 2008). An analysis of its photospheric activity, based on spot modelling techniques previously developed by our group for the analysis of the Sun as a star, shows that the active regions on CoRoT-2a arised within two active longitudes separated by about 180° and rotating with periods of 4.5221 and 4.5543 days, respectively, at epoch of CoRoT observations (112 continous days centered at ≈2007.6). We show that the total spotted area oscillates with a period of about 28.9 days, a value close to 10 times the synodic period of the planet with respect to the active longitude pattern rotating in 4.5221 days. Moreover, the variance of the stellar flux is modulated in phase with the planet orbital period. This suggests a possible star–planet magnetic interaction, a phenomenon already seen in other extrasolar planetary systems hosting hot-Jupiters.     

Updated results of a search for main-belt comets using the Canada–France–Hawaii Telescope Legacy Survey

The results of a search for main-belt comets using Canada–France–Hawaii Telescope Legacy Survey data are updated. The remaining observations in the Very Wide segment of data, taken in the g’ or r’ filters, are visually inspected for cometary activity. The number of main-belt objects in the original and new data sets are 11,438 and 13,802, respectively, giving a total number of 25,240. This is the largest, and least biased, search for main-belt comets to date. One object is observed to show cometary activity, and a new upper limit for strongly active main-belt comets is derived to be 40 ± 18.     

Solution of a Riemann–Hilbert problem for a new expression of Chandrasekhar’s H-function in radiative transfer

The linear singular integral equation derived from the nonlinear integral equation of Chandrasekhar’s H-function in radiative transfer is considered here to develop a new form of H-function as a solution of a Riemann–Hilbert problem using Plemelj and Cauchy integral formulae for complex domain. This new form of H-function is a simple integral of known functions. Forms of H-function both for conservative and nonconservative cases are obtained. Their numerical evaluations are made by Simpson’s one-third rule to arrive at an accuracy to ninth places of decimals.     

Improved nutation series for the non–rigid earth with a precise adjustment of parameters with nonlinear dependence

In this paper, the previous nutation series corresponding to the rotation of a non‐rigid earth composed of a rigid mantle and a liquid core obtained by Getino and Ferrándiz in 1997 are notably improved by using a high performance data fitting method. This method can be applied to many other problems presenting a non‐linear dependence on the free parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of a coupled approach for the solution of nonlinear singular initial value problems of Lane–Emden type

Lane–Emden type equations have been interesting since long time due to their wide applications in mathematical physics and astrophysics. In this paper, a coupled approach has been proposed for the solution of nonlinear singular value problems of Lane–Emden type.