Conrad Bertrand Tabi

We investigate the amplitude modulation of ion-acoustic wave packets in an unmagnetized electronegative plasma composed of cold positive ions, Boltzmann electrons, and negative ions following a Schamel trapped-particle distribution. The trapped-particle description is relevant to weakly collisional electronegative plasmas supporting Bernstein–Greene–Kruskal (BGK)-type potential structures and ion-hole equilibria, where a fraction of the negative-ion population can become trapped in the self-consistent wave potential. Unlike conventional analytic closures (Boltzmann, Tsallis, κ -distributed, nonthermal), which we show can only produce a cubic envelope nonlinearity regardless of their parametrization, this nonanalytic trapped-particle response naturally yields a generalized Schamel nonlinear Schrödinger equation combining the familiar cubic term with a genuinely noninteger | Ψ | 1 / 2 Ψ contribution. Derived through both a long-wavelength (Gardner-Schamel) limit and the full modulated-wave-packet limit, the resulting dispersion, cubic, and fractional coefficients are obtained in closed form. Two results stand out. First, the maximum modulational growth rate depends nonmonotonically on the negative-ion concentration, exhibiting an interior optimum that maximizes the instability above a critical temperature ratio, and, near the long-wavelength threshold, a finite concentration window outside of which the instability vanishes entirely. Second, a split-step Fourier analysis shows that the trapped-ion population breaks the time-symmetry of the Peregrine and Akhmediev rogue-wave solutions, causing them to build up faster than they decay, a signature invisible in the peak amplitude alone. These results extend previous electronegative plasma models and provide testable predictions for nonlinear wave localization in plasmas containing trapped particles.

We investigate memory-induced collective dynamics in a ring of electrically coupled Hindmarsh–Rose neurons operating in a chaotic bursting regime. The effects of long-range interactions, diffusion delay, reaction delay, and electromagnetic induction on spatiotemporal organization and Hamiltonian energy density are systematically analyzed. The dynamics is quantified using five complementary statistical indicators: the synchronization factor, the strength of incoherence, the discontinuity measure, the skewness measure, and the time-averaged Hamiltonian energy density. Depending on the memory parameters, the network exhibits asynchronous, chimera, multichimera, and synchronized states. We show that long-range interactions increase the Hamiltonian energy density and enhance the level of collective activity, although they predominantly generate asynchronous states when acting alone. Diffusion delay generates a rich variety of collective states, ranging from asynchronous and chimera patterns to complete synchronization depending on the interaction range, while reaction delay predominantly supports asynchronous, chimera, and multichimera dynamics. In contrast, electromagnetic induction promotes global synchronization from a critical memristive coupling threshold. Furthermore, the Hamiltonian energy density increases monotonically with the interaction range, reaction delay, and memristive feedback strength, whereas it exhibits a non-monotonic dependence on diffusion delay. These findings demonstrate that multiple memory mechanisms interact synergistically and competitively to shape neuronal coordination, energy localization, and pattern formation, providing new insights into the design of robust neuromorphic systems and brain-inspired algorithms.

This paper investigates modulational instability (MI) and the resulting nonlinear dynamics of plane waves in nematic liquid crystals with saturable competing nonlocal nonlinearities and fractional diffraction governed by the Lévy index. A modified fractional nonlinear Schrödinger model is developed, incorporating nonlocality, saturation, and competing reorientational and thermo-optic effects. Linear stability analysis provides an analytical expression for the MI growth rate, showing that the balance between effective nonlinearity and fractional diffraction governs instability. While thermal nonlinearity enhances MI, increased nonlocality, saturation, and larger Lévy indices suppress it. Symmetric and asymmetric nonlocal configurations are examined, with the latter displaying enhanced tunability of the instability spectrum. Numerical simulations confirm the analytical predictions and reveal the emergence of soliton trains, breathing modes, and localized structures. In particular, fractional diffraction can counteract nonlocal stabilization, enabling the restoration of MI in strongly nonlocal regimes. These findings demonstrate that the interplay of saturation, competing nonlinearities, and fractional dispersion provides a versatile mechanism for controlling instability and nonlinear wave evolution in optical media.

We consider a cigar-shaped Bose-Einstein condensate (BEC) of two-level atoms subjected to laser-induced Rabi coupling. By expanding the geometric vector potential to second order in the density-dependent fields and developing a quasi-one-dimensional (1D) reduction of the full three-dimensional problem via wave-function factorization, we derive an extended chiral Gross-Pitaevskii (GP) equation. We also derive traveling-wave solutions of the extended chiral GP equation using a projection (orthogonality) method, obtaining both bright and dark chiral solitons whose amplitudes and widths depend explicitly on the propagation direction. The chiral character of these solutions is confirmed through analytical analysis and numerical simulations. A BEC confined in a ring-shaped trap is also analyzed, leading to chiral soliton ring geometries. We show that a subtle interplay among density-dependent gauge potentials, confinement-induced interaction corrections, and higher-order current nonlinearities can give rise to alternative topological states, including chiral solitons and chiral ring solitons, in quasi-1D ultracold Bose gases. These results illustrate how higher-order corrections enrich BEC dynamics and provide means to control spatiotemporal structures in density-dependent condensates.