David Rollins

Heat transfer in an electrically conducting fluid over a stretching surface

Abstract An analysis is carried out to study the heat transfer characteristics in an electrically conducting fluid over a stretching sheet with variable wall temperature and internal heat generation or absorption. Two eases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed wall heat flux (PHF case). The solutions for the temperature, the heat transfer characteristics and their asymptotic limits for large Prandtl number (σ) are obtained in terms of Kummers and parabolic cylinder functions. It is shown that asymptotic limits are not possible for small Prandtl number; this is due to the solution changing by O(1) on length scale of 1/σ. For large Prandtl number, a boundary layer of width 1/σ at η = 0 and an internal layer of width ∝1/σ near the turning point are noticed.

Evolution of solitary-wave solution of the perturbed regularized long-wave equation

Abstract The evolution of the solitary-wave solution of the regularized long-wave (RLW) equation is considered. The perturbation is of the type that adds energy to the solitary wave. The perturbed solitary wave does not conserve “mass”. So, a tail is introduced of which the near-tail portion remedies this “mass” defect, while the far-tail portion exhibits a plateau structure.

Painlevé analysis and Lie group symmetries of the regularized long-wave equation

The Painleve formulation is given for the regularized long‐wave equation, which has been used to describe shallow water waves and drift waves in a plasma. The Lie group symmetries of the equation is then studied and it is shown that the only symmetries are due to the three conserved quantities.

Analytic aspects of the Zakharov–Kuznetsov equation

In this paper, we investigate some properties of the Zakharov–Kuznetsov equation (which describes nonlinear ion-acoustic waves in a magnetized plasma), including modulational stability of perturbations aligned with the field, conservation laws and integrability.

Generalized Painlevé formulation and Lie group symmetries of the Zakharov-Kuznetsov equation

Abstract In this paper, we give a generalized Painleve formulation for the Zakharov-Kuznetsov equation (which governs nonlinear ion-acoustic waves in a magnetized plasma). We will then study the Lie group symmetries of the same equation, and find that the latter possesses a five-parameter symmetry group.

The Painlevé formulations and exact solutions of the nonlinear evolution equations for modulated gravity wave trains

In this article the integrability aspects of the nonlinear evolution equations for modulated gravity wave trains are investigated by demanding the Painleve property of the solutions. The Painleve formulations also lead to kink‐shaped exact localized solutions of these equations.

Nonlinear propagation of two-dimensional gravity wave trains in magnetohydrodynamics

Nonlinear evolution of modulated two-dimensional gravity wave trains in a conducting fluid subject to a tangential applied magnetic field are considered. The effect of the applied magnetic field on the stability of the modulation and on the saturation amplitude in the long-time evolution are examined.

Magnetohydrodynamic boundary layer on a flat plate: Further analytic results

Further analytic results are deduced with the magnetohydrodynamic boundary layer equations for a flat plate. The asymptotic behavior of the solutions is deduced using the scaling group method. Then, an analytic perturbative procedure is used to determine an approximate solution that exhibits this asymptotic behavior.

The cauchy-poisson waves in an inviscid rotating stratified liquid☆

Abstract Based upon the Boussinesq approximation, an initial-value investigation is made of the axisymmetric Cauchy-Poisson waves generated in an inviscid, rotating, stratified liquid of infinite depth by the initially prescribed free-surface elevation. The asymptotic analysis of the integral solution is carried out by the stationary-phase method to describe the solution for large time and large distance from the source of the disturbance. The asymptotic solution is found to consist of the classical free-surface gravity waves and the internal-inertial waves.

An analytic perturbative solution for the Kadomtsev equation for a heavy atom in a very strong magnetic field

In this paper, we use a perturbative procedure due to Bender et al to solve analytically the Kadomtsev equation for a heavy atom in a very strong magnetic field.