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The governing equations for fluid flows, i.e. Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) model equations represent a water wave model. These model equations describe the bidirectional propagating water wave surface. In this paper, an auto-Bäcklund transformation is being generated by utilizing truncated Painlevé expansion method for the considered equation. This paper determines the new bright soliton solutions for $(2+1)$ and $(3+1)$-dimensional nonlinear KP-BBM equations. The simplified version of Hirota’s technique is utilized to infer new bright soliton solutions. The results are plotted graphically to understand the physical behavior of solutions.

The radial sensitivity of the elastic scattering of the weakly-bound ⁶Li and halo ⁶He nuclei on medium-mass ⁶⁴Zn target and heavy target ²⁰⁸Pb is examined around the Coulomb barrier energies. We present that very good agreement between theoretical and experimental results have been obtained with small χ²/N values. The fusion cross-section and volume integrals of the potentials have been deduced from the theoretical calculations for all studied systems at relevant energies. We have also analyzed the elastic scattering of the ⁶He+²⁰⁸Pb system at E_lab = 14, 16, 18, 22, 27 MeV in order to investigate whether there is a dispersion relation between the real and imaginary parts of the optical potential.

From dispersion relation approach, a formalism that describes final state interaction among three particles in a coupled-channel system is presented. Different representations of coupled-channel three-body formalism for spinless particles in both initial and final states are derived.

A new redshift formula is obtained considering the longitudinal Doppler effect in the de Sitter expanding universe where the relative geodesic motion is governed by the Lorentzian isometries of our new de Sitter relativity [I. I. Cotăescu, Eur. Phys. J. C 77, 485 (2017)]. This formula combines in a nontrivial manner the well-known cosmological contribution given by Lamaître’s law with that of the relative motion of the source with respect to a fixed observer as in de Sitter relativity instead of special relativity. Other related quantities as the dispersion relation, the propagation time of the photon and the real distance between the source and observer at the moment of observation are discussed pointing out their specific features in the de Sitter relativity.

New developments in both the theories and experiments related to the extraction of the top-row Cabibbo–Kobayashi–Maskawa matrix elements $V_{ud}$ and $V_{us}$ led to a series of new anomalies, for instance, the apparent violation of the top-row unitarity relation. It is important to further reduce all the associated Standard Model theory uncertainties in order to better understand whether such observations point towards the possibility of physics beyond the Standard Model, or rather some unexpectedly large Standard Model effects. This requires improved studies of tree-level and higher-order Standard Model corrections that enter the beta decays of pions, neutron, nuclei and kaons. We will briefly review the recent progress along this direction and discuss possible improvements in the future.

The screening length in a quark–gluon plasma, the dispersion relations of thermal gluon self-energy and the quark potential at high temperature are studied within the thermo field dynamics framework. By calculating the real and imaginary parts, of the gluon self-energy in one-loop order in thermo field dynamics, we obtain an expression for the screening length in a quark–gluon plasma and the dispersion relation between the real and imaginary parts. At high temperature, using photon exchange between electron-positron in a skeleton expansion and ladder approximation, the screened Coulomb potential and an expression for the screened quark potential is obtained.

In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern–Simons polarization tensor. In order to properly define the behavior of the quantum fields, the known UV/IR mixing due to radiative corrections is analyzed in the one-loop physical dispersion relation of the scalar and gauge fields.

In nonrelativistic systems, when there is spontaneous symmetry breaking, the number of Nambu–Goldstone bosons $(n_{\mathrm{\text{NG}}})$ are not necessarily equal to the number of broken generators $(n_{\mathrm{\text{BG}}})$. Here we use the method of operators for analyzing the necessary conditions in order to obtain the correct dispersion relation for the Nambu–Goldstone bosons.

The propagation characteristics of nonlinear TE surface waves at a lateral antiferromagnetic/nonmagnetic superlattices (LANS) substrate and a nonlinear magnetic cover have been investigated. LANS which are linear frequency-dependent gyromagnetic media, are described with an effective medium theory. It is found that the dispersion of the TE waves show the optical bistability behavior. The optical bistability is affected by the magnetic fraction f₁. We also calculate and illustrate the variation of the wave index with the power flow for various values of f₁. We found that the decrease in f₁ makes the power threshold of nonlinear TE surface waves decrease.

The paper is concerned with the propagation characteristics of TE surface waves in a planar wave-guide structure of a lateral antiferromagnetic-non magnetic super lattices (LANS) film bounded by a nonlinear dielectric cover and a left-handed substrate (LHM). In LHM substrate both permittivity and magnetic permeability are negative in definite frequency range. We study nonlinear dispersion properties of the TE surface waves and illustrate the power flow variation with the wave index in three different cases, i.e., when both permittivity and magnetic permeability are negative, when permittivity is negative and permeability is positive, and when both permittivity and magnetic permeability are positive.

In the first case, we found that surface waves are backward traveling and the wave power variation with the wave index shows bistability behavior. We also found that by increasing the film thickness the waves turn from forward to backward traveling in the second case. In the third case, surface waves are always forward traveling.

A theoretical investigation of TE nonlinear surface waves propagating in a photosensitive semiconductor-superconductor layers structure is fully described. The dispersion relation has been found and the effect of nonlinearity, operating angular frequency and the effect of temperature of the superconductor on the propagation characteristics have been examined. The power flow has also been studied. It has been shown that temperature and frequency increase the losses.

Magnetostatic surface waves have been investigated in a layered system of a nonlinear nonmagnetic negative permittivity material (NPM) and Ferrite (YIG). We derived the dispersion relation before numerically solving the dispersion relation of the TE nonlinear magnetostatic surface waves (NMSSW) in the proposed structure and the power flow. We found out that the wave effective nonlinear refractive index is much smaller in the forward direction than in the backward direction and consequently, the power flow is lower for the forward direction than the backward direction.

The stability characteristics of nonlinear surface waves propagating at a linear gyrodielectric substrate and a nonlinear dielectric cover have been simulated numerically by using the perturbation method. The growth rate of perturbation is computed by solving the dispersion equation of perturbation. We found that the nonlinear surface waves are unstable when their growth rate of perturbation is real, and stable when their growth rate of perturbation is imaginary. The spatial evolution of the steady-state field amplitude is determined using a computer simulation method.

Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second one rings have immediate contacts between each other. The dependence of the electron energy on the quasimomentum is obtained from the Schrödinger equation for the Bloch wavefunction. We have found an interesting feature of the system, namely, presence of discrete energy levels in the spectrum. The levels can be located in the gaps or in the bands depending on parameters of the system. The levels correspond to bound states and electrons occupying these levels are located on individual rings or couples of neighboring rings and do not contribute to the charge transport. The wavefunction for the bound states corresponding to the discrete levels is obtained. Modification of electron energy spectrum with variation of system parameters is discussed.

Tight-binding Hamiltonian on the prismatic pentagonal lattice is exactly solved to obtain the analytic expressions of dispersion relations and eigenvectors. This lattice is made of prismatic pentagon which is different from Cairo pentagon. Six different dispersion relations and total density of states are obtained. Dispersion relations are symmetric about the zero energy at a particular point in the parameter space. Although a large gap is found for the Cairo pentagonal lattice, no gap as well as no Dirac cone is found to appear in the tight-binding band structure for this prismatic pentagonal lattice. Instead, a pair of van Hove singularities has been identified at two different energy values in the band structure.

In this paper, a complete lattice study of thorium telluride (ThTe) in the effects of three-body interaction (TBI) in the framework of RIM and RSM models is reported. By use of the present model, I have theoretically reported elastic constants, pressure derivatives, dispersion relation curve, specific heat curve, combined density of states (CDS) and equation of state of the ThTe compound. The achieved results are good with experimentally reported results and have given very important information about this compound for further investigation.

A recent Bose–Einstein condensation (BEC) model of several cuprate superconductors is based on bosonic Cooper pairs (CPs) moving in 3D with a quadratic energy-momentum (dispersion) relation. The 3D BEC condensate-fraction versus temperature formula poorly fits penetration-depth data for two cuprates in the range 1/2<T/T_c≤1 where T_c is the BEC transition temperature. We show how these fits are dramatically improved, assuming cuprates to be quasi-2D, and how equally good fits are obtained for conventional 3D and quasi-1D nanotube superconducting data, provided the correct linear CP dispersion is assumed in BEC at their assumed corresponding dimensionalities. This is offered as additional concrete empirical evidence for linearly-dispersive pairs in another recent BEC scenario of superconductors within which a BCS condensate turns out to be a very special case.

A hybrid structure composed of a local resonance mass and an external oscillator is proposed in this paper for restraining the elastic longitudinal wave propagation. Theoretical model has been established to investigate the dispersion relation and band gaps of the structure. The results show that the hybrid structure can produce multi-band gaps wider than the multi-resonator acoustic metamaterials. It is much easier for the hybrid structure to yield wide and low band gaps by adjusting the mass and stiffness of the external oscillator. Small series spring constant ratio results in low-frequency band gaps, in which the external oscillator acts as a resonator and replaces the original local resonator to hold the band gaps in low frequency range. Compared with the one-dimensional phononic crystal (PC) lattice, a new band gap emerges in lower frequency range in the hybrid structure because of the added local resonance, which will be a significant assistance in low-frequency vibration and noise reduction. Further, harmonic response analysis using finite element method (FEM) has been performed, and results show that elastic longitudinal waves are efficiently forbidden within the band gaps.

This paper aims to study lump solutions to a class of (2+1)-dimensional nonlinear PDE systems, which involve the fourth-order Hirota derivative term: $D_t^2{D}_x{D}_y$. This Hirota derivative term generates higher-order derivatives of the temporal variable. Lump solutions to the resulting new class of nonlinear PDE systems are studied in detail via the Hirota bilinear method.

We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their rotation motion with their neighbors. It combines the Kuramoto model of synchronization and the Vicsek model of swarm formation. We study the mean-field kinetic and hydrodynamic limits of this system within two different scalings. In the small angular velocity regime, the resulting model is a slight modification of the "Self-Organized Hydrodynamic" model which has been previously introduced by the first author. In the large angular velocity case, a new type of hydrodynamic model is obtained. A preliminary study of the linearized stability is proposed.