Purpose The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme. Design/methodology/approach The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities. Findings The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients. Originality/value The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

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PurposeThe purpose of this paper is to model an important aspect of the problem of sensor information integration that arises in wireless communications, where N sensors try to communicate with a receiver using a single un‐shareable radio channel. If several sensors transmit at the same time, their transmissions collide at the receiver resulting in garbled messages and the need for re‐transmission. This is highly undesirable since the sensors are energy‐constrained and the radio interface is known to be the most significant source of energy expenditure. Consequently, it is of paramount importance to design arbitration protocols that are highly efficient in stamping out collisions and that are, at the same time, as lightweight as possible.Design/methodology/approachThe receiver advertises a time division multiple access (TDMA) frame consisting of n slots, numbered from 1 to n, where n is an application‐dependent parameter. Each sensor generates uniformly at random, and independently of other sensor, an integer i between 1 and n and transmits in the i‐th slot of the TDMA frame. If two or more sensors are transmitting in the same slot their messages will be lost to collision. Similarly, slots that carry no transmission are wasted. The authors model the arbitration strategy discussed above as a Bose‐Einstein occupancy problem where N indistinguishable balls are thrown at random into n distinguishable bins and all distinguishable outcomes are considered to be equally likely.FindingsIn this paper the authors present a distributed probabilistic mechanism that aims to arbitrate between several competing requests by various sensors for the radio channel. The mechanism is simple, energy‐efficient and does not rely on the existence of unique sensor identifiers (IDs).Originality/valueThe Bose‐Einstein occupancy model presented in this paper will help the receiver to tailor an appropriate number of timeslots in TDMA frame during the integration process, such that collisions are minimized, and hence integration between sensors can be done effectively.

This paper revisits the comrade matrix approach in finding the greatest common divisor (GCD) of two orthogonal polynomials. The present work investigates on the applications of the QR decomposition with iterative refinement (QRIR) to solve certain systems of linear equations which is generated from the comrade matrix. Besides iterative refinement, an alternative approach of improving the conditioning behavior of the coefficient matrix by normalizing its columns is also considered. As expected the results reveal that QRIR is able to improve the solutions given by QR decomposition while the normalization of the matrix entries do improves the conditioning behavior of the coefficient matrix leading to a good approximate solutions of the GCD.