Modern Physics Letters B

Under investigation in this letter is a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters $h_1$, $h_3$ and $h_5$ which are all the real constants: When $h_1$ increases, amplitude of the lump wave increases, and location of the peak moves; when $h_3$ increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when $h_5$ changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.

Under investigation in this letter is a variable-coefficient (3+1)-dimensional generalized shallow water wave equation. Bilinear form and Bäcklund transformation are obtained. One-, two- and three-soliton solutions are derived via the Hirota bilinear method. Interaction and propagation of the solitons are discussed graphically. Stability of the solitons is studied numerically. Soliton amplitude is determined by the spectral parameters. Soliton velocity is not only related to the spectral parameters, but also to the variable coefficients. Phase shifts are the only difference between the two-soliton solutions and the superposition of the two relevant one-soliton solutions. Numerical investigation on the stability of the solitons indicates that the solitons could resist the disturbance of small perturbations and propagate steadily.

Under investigation in this letter is a (2+1)-dimensional Sawada-Kotera equation. With the aid of the bilinear forms derived from the Bell polynomials, the Nth-order soliton solutions are obtained via the Pffafian method, and breather solutions are derived with the ansätz method. Analytic solutions obtained via the Pffafian method are the bell-type solitons. Two different kinds of the homoclinic breathers are seen, one of which is real and the other of which is complex, with two breathers interacting with each other. Homoclinic breather wave can evolve periodically along a straight line with a certain angle with the x axis and y axis, and its velocity, amplitude and width remain unchanged during the propagation. Homoclinic breather wave is not only space-periodic but also time-periodic. Interaction between the two breathers is elastic, which is similar to that of the solitons.

Under investigation are the soliton interactions for a (2+1)-dimensional nonlinear Schrödinger equation, which can describe the dynamics of a nonlinear photonic quasi-crystal or vortex Airy beam in a Kerr medium. With the symbolic computation and Hirota method, analytic bright N-soliton and dark two-soliton solutions are derived. Graphic description of the soliton properties and interactions in a nonlinear photonic quasicrystal or Kerr medium is done. Through the analysis on bright and dark one solitons, effects of the optical wavenumber/linear opposite wavenumber and nonlinear coefficient on the soliton amplitude and width are studied: when the absolute value of the optical wavenumber or linear opposite wavenumber increases, bright soliton amplitude and dark soliton width become smaller; nonlinear coefficient has the same influence on the bright soliton as that of the optical wavenumber or linear opposite wavenumber, but does not affect the dark soliton amplitude or width. Overtaking/periodic interactions between the bright two solitons and overtaking interactions between the dark two solitons are illustrated. Overtaking interactions show that the bright soliton with a larger amplitude moves faster and overtakes the smaller, while the dark soliton with a smaller amplitude moves faster and overtakes the larger. When the absolute value of the optical wavenumber or linear opposite wavenumber increases, the periodic-interaction period becomes longer. All the above interactions are elastic. Through the interactions, soliton amplitudes and shapes keep invariant except for some phase shifts.

For the (3+1)-dimensional nonlinear evolution equation in a plasma, crystal or fluid, the Pfaffian solutions are obtained via the Bell polynomials, symbolic computation and Hirota method. Amplitudes and velocities of the solitons are discussed, respectively, as well as the conditions on whether the collisions are overtaking or head-on in the fluid/plasma/crystal. If the product of four wave numbers is greater than 0, collisions are overtaking, or else, head-on. For the (2+1)-dimensional Sawada–Kotera equation in a liquid, we discuss that amplitudes and velocities of the solitons, as well as the conditions of solitonic collisions. Hereby, there only exist the overtaking collisions between the solitons in such a liquid because the sign of $l_1+l_2$ is the same as $l_1^3+l_2^3$, where $l_1$ and $l_2$ are the wave numbers in the liquid. Figures showing the overtaking and head-on collisions for the two and three solitons in the fluid/plasma/crystal are also presented.

Korteweg-de Vries (KdV)-type equations are seen to describe the shallow-water waves, lattice structures and ion-acoustic waves in plasmas. Hereby, we consider an extension of the KdV-type equations called the generalized (2+1)-dimensional Nizhnik–Novikov–Veselov equations with variable coefficients in an inhomogeneous medium. Via the Hirota bilinear method and symbolic computation, we derive the bilinear forms, N-soliton solutions and Bäcklund transformation. Effects of the first- and higher-order dispersion terms are investigated. Soliton evolution and interaction are graphically presented and analyzed: Both the propagation velocity and direction of the soliton change when the dispersion terms are time-dependent; The interactions between/among the solitons are elastic, independent of the forms of the coefficients in the equations.

The finite element method is used here to investigate the vibrational behavior of single-walled boron nitride nanotube/polymer nanocomposites. The polymer matrix is modeled as a continuous media. Besides, nanotubes are modeled as a space-frame structure. It is shown that increasing the length of nanotubes at a constant volume fraction leads to decreasing of the nanocomposite frequency. By investigating the effect of volume percentage on the frequencies of the boron nitride nanotube-reinforced polymer nanocomposites, it is observed that for short nanotubes, the nanocomposites with larger nanotube volume fractions have larger frequencies. Also, through studying the first 10 frequencies of nanocomposites reinforced by armchair and zigzag nanotubes, it is shown that the effect of chirality on the vibrational behavior of nanocomposite is insignificant.

The heat currents and thermal rectification in a non-equilibrium spin-chain system with multi-spin interaction and external field are investigated. The influence of system parameters, including mean temperature, temperature difference, external field and multi-spin interaction, on heat currents and thermal rectification are studied. We show that the magnitude of heat currents and thermal rectification can be controlled by varying these parameters. Particularly, by increasing the intensity of multi-spin interaction and external field, two kinds of blockade phenomena can be observed, i.e. the thermal blockade and the energy blockade. Besides, the physical origin of thermal rectification and the blockade phenomena are explored. In addition, the present results may provide a useful approach to the controlling of heat currents when there exists multi-spin interaction in the system.

Carbon dioxide (CO₂) as the primary greenhouse gas, is the main pollutant that is warming earth. CO₂ is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO₂ emission. To this end, this study investigates the behavior of CO₂ in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO₂ density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO₂ decreases and very low concentration of CO₂ molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.

Understanding the structural characteristics of urban traffic network comprehensively can provide references for improving road utilization rate and alleviating traffic congestion. This paper focuses on the spatial-temporal correlations between different pairs of traffic series and proposes a complex network-based method of constructing the urban traffic network. In the network, the nodes represent road segments, and an edge between a pair of nodes is added depending on the result of significance test for the corresponding spatial-temporal correlation. Further, a modified PageRank algorithm, named the geographical weight-based PageRank algorithm (GWPA), is proposed to analyze the spatial distribution of important segments in the road network. Finally, experiments are conducted by using three kinds of traffic series collected from the urban road network in Beijing. Experimental results show that the urban traffic networks constructed by three traffic variables all indicate both small-world and scale-free characteristics. Compared with the results of PageRank algorithm, GWPA is proved to be valid in evaluating the importance of segments and identifying the important segments with small degree.