Band 66, Heft 6-7

The Kadomtsev-Petviashvili and Boussinesq equations (u xxx -6uu x )x -u tx ±u yy = 0; (u xxx - 6uu x ) x +u xx ±u tt = 0; are completely integrable, and in particular, they possess the three-soliton solution. This article aims to expose a uniqueness property of the Kadomtsev-Petviashvili (KP) and Boussinesq equations in the integrability theory. It is shown that the Kadomtsev-Petviashvili and Boussinesq equations and their dimensional reductions are the only integrable equations among a class of generalized Kadomtsev-Petviashvili and Boussinesq equations (u x1x1x1 - 6uu x1 ) x1 + Σ M i;j=1aijuxixj = 0; where the a ij ’s are arbitrary constants and M is an arbitrary natural number, if the existence of the three-soliton solution is required

With the help of a Cole-Hopf transformation, the nonlinear Burgers system in (3+1) dimensions is reduced to a linear system. Then by means of the linear superposition theorem, a general variable separation solution to the Burgers system is obtained. Finally, based on the derived solution, a new type of localized structure, i.e., a solitonic bubble is revealed and some evolutional properties of the novel localized structure are briefly discussed

The exact chirped soliton-like and quasi-periodic wave solutions of the (3+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behaviour of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss)

We establish necessary optimality conditions for variational problems with an action depending on the free endpoints. New transversality conditions are also obtained. The results are formulated and proved using the recent and general theory of time scales via the backward nabla differential operator

By means of the linear approximation method, the output intensity power and signal-to-noise ratio (SNR) of a single-mode laser driven by sine-squared pulse modulation correlated noise are calculated. The effects of amplitude B, period T, and width t on the resonance curves of SNR to the pump noise intensities and quantum noise intensities of pulse are discussed, and it is found that the SNR shows a stochastic resonance with the varying of pulse width τ

We performed a study for the flow of a Maxwell fluid induced by a stretching surface. Heat transfer is also addressed by using the convective boundary conditions. We solved the nonlinear problem by employing a homotopy analysis method (HAM).We computed the velocity, temperature, and Nusselt number. The role of embedded parameters on the velocity and temperature is particularly analyzed

Although the decomposition method and its modified form were used during the last two decades by many authors to investigate various scientific models, a little attention was devoted for their applications in the field of fluid mechanics. In this paper, the Adomian decomposition method (ADM) is implemented for solving the nonlinear partial differential equation (PDE) describing the peristaltic flow of a power-law fluid in a circular cylindrical tube under the effect of a magnetic field. The numerical solutions obtained in this paper show the effectiveness of Adomian’s method over the perturbation technique

A mathematical model will be analyzed in order to study the effects of viscous dissipation and Ohmic heating (Joule heating) on magnetohydrodynamic (MHD) natural convection flow of a temperature dependent viscosity from heated vertical wavy surface. The present physical problem is studied numerically by using the appropriate variables, which reduce the complex wavy surface into a flat one. An implicit marching Chebyshev collocation scheme is employed for the analysis. Numerical solutions are obtained for velocity, temperature, local skin friction, and Nusselt number for a selection of parameter sets consisting of Eckert number, Prandtl number, MHD variation, and amplitude-wavelength ratio parameter. Numerical results show that these parameters have significant influences on the velocity and the temperature profiles as well as for the local skin friction and Nusselt number

In this paper, we describe a new method for constructing a canal surface surrounding a timelike horizontal biharmonic curve in the Lorentzian Heisenberg group Heis 3 . Firstly, we characterize timelike biharmonic curves in terms of their curvature and torsion. Also, by using timelike horizontal biharmonic curves, we give explicit parametrizations of canal surfaces in the Lorentzian Heisenberg group Heis 3

A generic nonlinear Maxwell model for the stress tensor in viscoelastic materials is studied under mixing scenarios in a three-dimensional steady lid-driven cavity flow. Resulting laminar and turbulent flow profiles are investigated to study their mixing efficiencies. Massless tracer particles and passive concentrations are included to show that the irregular spatio-temporal chaos, present in turbulent flow, is useful for potential mixing applications. A Lyapunov measure for filament divergence confirms that the turbulent flow is more efficient at mixing

This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I 15=2 of the trivalent erbium ion splits into three Stark quartets Γ 8 and two different doublets Γ 6 and Γ 7 (irreducible representations). The CF energy matrix of the Er 3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ 6 and Γ 7 , respectively