Combining planted drying beds to maturation ponds at pilot scale for a comprehensive treatment of faecal sludge in sub-Saharan Africa.

Hight birth rate in developing countries generates huge amounts of faecal sludge to treat at a given time. In sub-Saharan Africa, it is estimated that 95% of households are not connected to a sewerage system for excreta disposal, and faecal sludge treatment of plants is almost absent, thus the necessity of developing cost-effective technologies to contain their harmful effect. In response to this preoccupation, pilot scale experiments combining drying beds with maturation ponds were conducted in Yaounde (Cameroon) for the treatment of faecal sludge.

Engineering rogue waves with quintic nonlinearity and nonlinear dispersion effects in a modified Nogochi nonlinear electric transmission network.

A one-dimensional modified Nogochi nonlinear electric transmission network with dispersive elements that consist of a large number of identical sections is theoretically studied in the present paper. The first-order nonautonomous rogue waves with quintic nonlinearity and nonlinear dispersion effects in this network are predicted and analyzed using the cubic-quintic nonlinear Schrödinger (CQ-NLS) equation with a cubic nonlinear derivative term. The results show that, in the semidiscrete limit, the voltage for the transmission network is described in some cases by the CQ-NLS equation with a derivative term that is derived employing the reductive perturbation technique.

Transmission of rogue wave signals through a modified Noguchi electrical transmission network.

A distributed electrical transmission network with dispersive elements that consists of a large number of identical unit cells is considered. Using the reductive perturbation method in the semidiscrete limit, we show that the voltage for the network is described by a nonlinear Schrödinger (NLS) equation with an external linear potential. Using such a NLS equation, the propagation of the first- and second-order rogue waves in the system is predicted and analyzed quantitatively and qualitatively.

Management of matter-wave solitons in Bose-Einstein condensates with time-dependent atomic scattering length in a time-dependent parabolic complex potential.

In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establish the integrability conditions under which analytical solutions describing the modulational instability and the propagation of both bright and dark solitary waves on a continuous wave background are obtained. The obtained integrability conditions also appear as the conditions under which the solitary waves of the BECs can be managed by controlling the functional gain or loss parameter.

Solitonlike pulses along a modified Noguchi nonlinear electrical network with second-neighbor interactions: Analytical studies.

A modified lossless nonlinear Noguchi transmission network with second-neighbor interactions is considered. In the semidiscrete limit, we apply the reductive perturbation method and show that the dynamics of modulated waves propagating through the network are governed by an NLS equation with linear external potential. Classes of exact solitonic solutions of this network equation are derived, proving possible transmission of both bright and dark solitonlike pulses through the network.

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential.

A lossless nonlinear LC transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed.

Bioheat transfer problem for one-dimensional spherical biological tissues.

Based on the Pennes bioheat transfer equation with constant blood perfusion, we set up a simplified one-dimensional bioheat transfer model of the spherical living biological tissues for application in bioheat transfer problems. Using the method of separation of variables, we present in a simple way the analytical solution of the problem. The obtained exact solution is used to investigate the effects of tissue properties, the cooling medium temperature, and the point-heating on the temperature distribution in living bodies.

Dynamics of modulated waves in a lossy modified Noguchi electrical transmission line.

We study analytically the dynamics of modulated waves in a dissipative modified Noguchi nonlinear electrical network. In the continuum limit, we use the reductive perturbation method in the semidiscrete limit to establish that the propagation of modulated waves in the network is governed by a dissipative nonlinear Schrödinger (NLS) equation. Motivated with a solitary wave type of solution to the NLS equation, we use both the direct method and the Weierstrass's elliptic function method to present classes of bright, kink, and dark solitary wavelike solutions to the dissipative NLS equation of the network.

Analytical study of dynamics of matter-wave solitons in lossless nonlinear discrete bi-inductance transmission lines.

We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave.

Phase engineering, modulational instability, and solitons of Gross-Pitaevskii-type equations in 1+1 dimensions.

Motivated by recent proposals of "collisionally inhomogeneous" Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we introduce a phase imprint into the macroscopic order parameter governing the dynamics of BECs with spatiotemporal varying scattering length described by a cubic Gross-Pitaevskii (GP) equation and then suitably engineer the imprinted phase to generate the modified GP equation, also called the cubic derivative nonlinear Schrödinger (NLS) equation. This equation describes the dynamics of condensates with two-body (attractive and repulsive) interactions in a time-varying quadratic external potential. We then carry out a theoretical analysis which invokes a lens-type transformation that converts the cubic derivative NLS equation into a modified NLS equation with only explicit temporal dependence.

Transverse stability of solitary waves propagating in coupled nonlinear dispersive transmission lines.

In the semidiscrete limit and in suitably scaled coordinates, the voltage of a system of coupled nonlinear dispersive transmission lines is described by a nonlinear Schrödinger equation. This equation is used to study the transverse stability of solitary waves of the system. Exact results for the growth rate and the corresponding perturbation function of linear transverse perturbations are obtained in terms of the network's and soliton's parameters.

Modulational instability criteria for coupled nonlinear transmission lines with dispersive elements.

We investigate the modulational instability of Stokes wave solutions on a system of coupled nonlinear electrical transmission lines with dispersive elements. In the continuum limit, and in suitable scaled coordinates, the voltage on the system is described by the two-dimensional coupled nonlinear Schrödinger equations. The set of coupled nonlinear Schrödinger equations obtained is analyzed via a perturbation approach.

Exact solutions of the derivative nonlinear Schrödinger equation for a nonlinear transmission line.

We consider the derivative nonlinear Schrödinger equation with constant potential as a model for wave propagation on a discrete nonlinear transmission line. This equation can be derived in the small amplitude and long wavelength limit using the standard reductive perturbation method and complex expansion. We construct some exact soliton and elliptic solutions of the mentioned equation by perturbation of its Stokes wave solutions.