The present manuscript uses three Kudryashov-based methods to analytically inspect the class of Gerdjikov–Ivanov equations, which comprises the standard Gerdjikov–Ivanov equation and the perturbed Gerdjikov–Ivanov equation. Various optical solitonic solutions have been constructed. Certainly, as the reported solitonic structures happened to be exponential functions, diverse true solitonic solutions can easily be resorted to upon suitably fixing the involving parameters, including mainly the bright and singular solitons. Lastly, the study graphically examined some of the constructed structures, which were then found to portray some interesting known shapes in the theory of solitary waves and nonlinear Schrödinger equations. Additionally, the Kudryashov-index d has been noted to play a significant role in the propagation of complex waves in the nonlinear media described by Gerdjikov–Ivanov equations.

In this paper, the Lie symmetry analysis method is applied to the time-fractional Boussinesq–Burgers system which is used to describe shallow water waves near an ocean coast or in a lake. We obtain all the Lie symmetries admitted by the system and use them to reduce the fractional partial differential equations with a Riemann–Liouville fractional derivative to some fractional ordinary differential equations with an Erdélyi–Kober fractional derivative, thereby getting some exact solutions of the reduced equations. For power series solutions, we prove their convergence and show the dynamic analysis of their truncated graphs. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.

The (2 + 1)-dimensional generalized fifth-order KdV (2GKdV) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero background wave on the multiple soliton solution of the 2GKdV equation, breather waves are constructed, for which some transformed wave conditions are considered that yield abundant novel nonlinear waves including X/Y-Shaped (XS/YS), asymmetric M-Shaped (MS), W-Shaped (WS), Space-Curved (SC) and Oscillation M-Shaped (OMS) solitons. Furthermore, distinct nonlinear wave molecules and interactional structures involving the asymmetric MS, WS, XS/YS, SC solitons, and breathers, lumps are constructed after considering the corresponding existence conditions. The dynamical properties of the nonlinear molecular waves and interactional structures are revealed via analyzing the trajectory equations along with the change of the phase shifts.

The rotating shallow water system is an important physical model, which has been widely used in many scientific areas, such as fluids, hydrodynamics, geophysics, oceanic and atmospheric dynamics. In this paper, we extend the application of the Adomian decomposition method from the single equation to the coupled system to investigate the numerical solutions of the rotating shallow water system with an underlying circular paraboloidal basin. By introducing some special initial values, we obtain interesting approximate pulsrodon solutions corresponding to pulsating elliptic warm-core rings, which take the form of realistic series solutions. Numerical results reveal that the numerical pulsrodon solutions can quickly converge to the exact solutions derived by Rogers and An, which fully shows the efficiency and accuracy of the proposed method. Note that the method proposed can be effectively used to construct numerical solutions of many nonlinear mathematical physics equations. The results obtained provide some potential theoretical guidance for experts to study the related phenomena in geography, oceanic and atmospheric science.

A set of orthogonal product states is deemed genuinely nonlocal if they remain locally indistinguishable under any bipartition. In this paper, we first construct a genuinely nonlocal product basis B_I(5, 3) in ${{\mathbb{C}}}^{5}\otimes {{\mathbb{C}}}^{5}\otimes {{\mathbb{C}}}^{5}$ using a set of nonlocal product states in ${{\mathbb{C}}}^{3}\otimes {{\mathbb{C}}}^{4}$. Then, we obtain a genuinely nonlocal product basis B_II(5, 3) by replacing certain states in B_I(5, 3) with some superposition states. We achieve perfect discrimination of the constructed genuinely nonlocal product basis, separately employing two EPR states and one GHZ state. Our protocol is more efficient than quantum teleportation.

Quantum coherence, as a more general quantum resource compared to quantum entanglement, has attracted increasing attention over recent years. Establishing stable quantum coherence is crucial for implementing reliable quantum information tasks. In this study, we propose a scheme to generate stable quantum coherence of two qubits via an epsilon-near-zero (ENZ) waveguide. We find that employing Si₃N₄ rather than SiO₂ results in stronger qubit-qubit coupling and maximal quantum coherence in a certain range. We derive analytical expressions for both quantum coherence and quantum entanglement, allowing for direct comparison within a unified framework. To achieve stable quantum coherence, classical field driving is introduced. We find that stable coherence is much larger and easier mediated than that of stable entanglement. Our work contributes to the creation of a new stable quantum resource via an ENZ waveguide.

Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. Recently, theoretical and experimental simulations of two-anyon states in a one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, resulting in non-physical degrees of freedom. In the present work, we deduce finite difference equations for the two-anyon state in a one-dimensional lattice by solving the Schrödinger equation with orthogonal and complete basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates, while the conventional (non-orthogonal) method produces many non-physical redundant eigensolutions whose components violate the anyonic commutation relations. The dynamical property of the two-anyon states in a sufficiently large lattice is investigated and compared in both the orthogonal and conventional schemes. For initial states with two anyons at the same site or two (next-)neighboring sites, we observe the same dynamical behavior in both schemes, including the revival probability, probability density function and two-body correlation. For other initial states, the conventional scheme produces erroneous states that no longer obey the anyonic relations. The period of Bloch oscillations in the pseudo-fermionic limit has been found to be twice that in the bosonic limit, while these oscillations disappear at other statistical parameters. Our findings are vital for quantum simulations of few-body anyonic physics in lattice models.

Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.

The improved quantum molecular dynamics model was employed to study the ²³⁸U+²³⁸U multinucleon transfer reaction at E_c.m. = 833 MeV in this work. The influence of the orientation effect on the nuclear deformation at the contact moment, the composite system lifetime, the transfer rate and the fragment production mechanism are investigated. Statistical analysis reveals that at the contact moment, the orientation of the projectile and the target have less influence on each other and retain their respective initial characteristics to some extent. For collision parameters less than 6 fm, significant differences are observed in composite system lifetime and transfer rate under different orientation configurations; however, the orientation effect gradually diminishes with increasing collision parameters. Additionally, it is found that transfer reactions dominate when the collision parameter b ≤ 6 fm, while elastic and inelastic scattering events increase rapidly as the collision parameter exceeds 6 fm. Within the range of 10 ≤ b ≤ 13 fm, the transfer probability for side–side collisions is significantly higher compared to other cases.

This investigation assesses the feasibility of a traversable wormhole by examining the energy densities associated with charged Casimir phenomena. We focus on the influence of the electromagnetic field created by an electric charge as well as the negative energy density arising from the Casimir source. We have developed different shape functions by defining energy densities from this combination. This paper explores various configurations of Casimir energy densities, specifically those occurring between parallel plates, cylinders and spheres positioned at specified distances from each other. Furthermore, the impact of the generalized uncertainty principle correction is also examined. The behavior of wormhole conditions is evaluated based on the Gauss–Bonnet coupled parameter (μ) and electric charge (Q) through the electromagnetic energy density constraint. This is attributed to the fact that the electromagnetic field satisfies the characteristic ρ = −p_r. Subsequently, we examine the active gravitational mass of the generated wormhole geometries and explore the behavior of μ and Q concerning active mass. The embedding representations for all formulated shape functions are examined. Investigations of the complexity factor of the charged Casimir wormhole have demonstrated that the values of the complexity factor consistently fall within a particular range in all scenarios. Finally, using the generalized Tolman–Oppenheimer–Volkoff equation, we examine the stability of the resulting charged Casimir wormhole solutions.

The main objective of this paper is to reveal the evolving traversable wormhole solutions in the context of modified $f({ \mathcal R },{ \mathcal G })$ gravity, which affects the gravitational interaction. These results are derived by applying the Karmarkar condition, which creates wormhole geometry that meets the necessary conditions and connects two asymptotically flat areas of spacetime. The proposed study's main goal is to construct the wormhole structures by splitting the $f({ \mathcal R },{ \mathcal G })$ gravity model into two forms Firstly, we split the model into an exponential-like $f({ \mathcal R })$ gravity model and a power law $f({ \mathcal G })$ gravity model, and secondly, we consider the Starobinsky $f({ \mathcal R })$ gravity model along with a power law $f({ \mathcal G })$ gravity model. Besides, we address the feasibility of shape functions and the structural analysis of wormhole structures for specific models. These models are then confined to be compatible with current experimental evidence. Further, the energy conditions of the wormhole are geometrically probed, and it is proven that they adhere to the null energy conditions in areas close to the throat. Moreover, the fascinating aspect of this study involves conducting an examination and comparison of evolving wormhole geometries in the vicinity of the throat in our chosen models, utilizing two- and three-dimensional graphical representations. We observe that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter, correlating to the proper choice of $f({ \mathcal R },{ \mathcal G })$ gravity models and acceptable free parameter values. In summary, we conclude that our findings meet all the criteria for the existence of wormholes, affirming the viability and consistency of our study.

In this work, we investigate the numerical evolution of massive Kaluza–Klein (KK) modes of a Dirac field on a thick brane. We deduce the Dirac equation in five-dimensional spacetime, and obtain the time-dependent evolution equation and Schrödinger-like equation of the extra-dimensional component. We use the Dirac KK resonances as the initial data and study the corresponding dynamics. By monitoring the decay law of the left- and right-chiral KK resonances, we compute the corresponding lifetimes and find that there could exist long-lived KK modes on the brane. Especially, for the lightest KK resonance with a large coupling parameter and a large three momentum, it will have an extremely long lifetime.

The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated. The Sagdeev technique was employed, and an energy equation was derived. Our findings show that the proposed system reveals the existence of a double-layer solution, periodic, supersoliton, and superperiodic waves. The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves. It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model. Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.

We investigate spatiotemporal periodic patterns in harmonically trapped Bose–Einstein condensates (BECs) driven by a periodic modulation of the interaction. Resonant with the breathing mode, we show the emergence of a square lattice pattern containing two orthonormal stripes. We study the time evolutions of the lattice patterns for different driving strengths and dissipations. We find that its spatial periodicity and temporal oscillating frequency match the Bogoliubov dispersion, which is the intrinsic property of the system and relevant to the parametric amplification of elementary excitations. In the circumstances of strong driving strength and low dissipation, we further observe the triad interaction and the resulting superlattice state, which are well explained by the nonlinear amplitude equation for superimposed stripes. These results shed light on unexplored nonlinear spatiotemporal dynamics of two-dimensional patterns in harmonically trapped BECs that can pave the way for engineering exotic patterns by state-of-the-art experiments.

This investigation focuses on the under-damped Brownian transport of a dimer characterized by two harmonically interacting components. The friction coefficients between the dimer components are different; thus the dynamic symmetry of the system is broken. In addition, the inertial ratchets are synchronously modulated by the feedback control protocol in time. Here, we analyze the transport performance by studying the average velocity and energy conversion efficiency of the dimer induced by friction symmetry breaking and external forces. Furthermore, we can also identify the enhancement of the centre-of-mass mean velocity and energy conversion efficiency of inertial frictional ratchets for intermediate values of the driving amplitude, coupling strength and damping force. Remarkably, in the weak bias case, the directed transport of inertial Brownian particles can be reversed twice by modulating the suitable friction of the dimer. In particular, the frictional ratchets can acquire a series of resonant steps under the influence of harmonic force. These conclusions of reliable transport in noisy environments are expected to provide insights into the performance of natural molecular motors.

In this work, we studied the electronic and magnetic properties of the double perovskite Sr₂CrMoO₆ using ab initio calculations with generalized gradient approximation (GGA) and Monte Carlo (MC) simulations. The compound has two magnetic sublattices: one occupied by Mo⁵⁺ with spin ($S=\tfrac{1}{2}$) and the other by Cr³⁺ with spin ($\sigma =\tfrac{3}{2}$). The results showed half-metallic behavior with a total magnetic moment of 2.0 μ_B. Using Monte Carlo simulations, we investigated the phase transitions and observed interesting phenomena such as a critical endpoint and both second-order and first-order phase transitions. Additionally, the results revealed compensation points for specific values of the crystal field.

Kelvin's circulation, as a loop integral of the velocity field, is first shown to be equal to ${{\rm{\Gamma }}}_{{ \mathcal C }}=2\pi {\rm{\Delta }}n{{\rm{\Gamma }}}_{1}+{\rm{constant}}$ in an inviscid fluid, with Γ₁ a unit circulation. The integer Δn is interpreted as the number of net 2π-rotations of the velocity vector in one cyclicality along the circulation loop and hence it is a topological number. Different from the linkage number in the helicity invariant, which only exists in 3D space, the topological number in the circulation invariant is independent of the spatial dimension. A further study reveals that this new topological phase 2πΔn is rooted at the gauge invariance of the circulation and it is a counterpart of the Berry's phase in the quantum system.