In this study, the conformable coupled nonlinear Maccari system (CCNMS) is analyzed by employing a modified ( G'G^2) -expansion technique. This method offers a systematic way to derive exact analytical traveling-wave solutions of the system. A wide class of closed-form solutions is obtained, encompassing trigonometric, hyperbolic, rational, and kink-type structures that reveal diverse nonlinear phenomena such as solitons and hybrid waves. The solutions, presented in compact analytical expressions, cover various parameter regimes and exhibit both mathematical simplicity and rich structural features. Their qualitative behaviors are illustrated using symbolic computations performed in Mathematica and MATLAB. Furthermore, a bifurcation analysis of the reduced ordinary differential equation is carried out to determine the conditions leading to periodic, solitary, and homoclinic wave formations.The results contribute to a deeper theoretical understanding of nonlinear wave propagation and demonstrate the relevance of CCNMS in areas such as fluid dynamics, nonlinear optics, magnetization, and Bose–Einstein condensates. The proposed framework can also be adapted to other types of conformable fractional partial differential equations.
The Kaup–Kupershmidt equation is used to study nonlinear wave propagation associated with ocean currents, capturing the combined effects of nonlinearity and dispersion. Due to the many solitons exhibited by the fractional Kaup–Kupershmidt (K–K) equation, which represent the many solitary waves observed in ocean currents, plasma physics, and optics, several analytical methods have been developed and consistently applied to study these phenomena. One such method is the homogeneous balance method (HBM), which invariably relies on the embedded Riccati equation. Thus, the workability of the HBM largely depends on the embedded Riccati equation, which by and large determines the number and type of solitons yielded when the HBM is applied to the fractional K–K equation. Undeniably, several Riccati equations appear in the literature, each with unique properties. Therefore, if the HBM is embedded with a particular Riccati equation for solving the fractional K–K equation, the underlying mechanisms of the solitary waves in ocean current, plasma physics and optics are unveiled. The HBM and its modified methods explored only by the researchers have not been exhaustively observed a fractional Riccati equation with a quadratic term as the dependent variable, where coefficient of the second term is one and coefficient of the linear term is zero, d^γϕ/dξ ^γ = p + ϕ ^2(ξ ), quadratic term as the dependent variable and applied this modified homogeneous balance method (MHBM) to obtain the exact solitons of the fractional K–K equation. Applying the MHBM in solving the fractional K–K equation yielded five solitons: a bright soliton with a flat top, a gray soliton, a dark soliton with a flat bottom, an L-tilted soliton, and a halfway dark soliton. Three of the five solitons, a bright soliton with a flat bottom, a dark soliton with a flat bottom, and an L-tilted soliton, were new solitons that have not been observed in literature. These three new solitons of the fractional K–K equation have been observed in this paper as a result of a new embedded Riccati equation in HBM. The soliton properties, such as the kinetic and potential energies of the gray soliton and L-tilted soliton, are similar, whereas in the bright soliton and in the flat top and dark soliton with flat bottom, the potential and kinetic energies are in opposite directions. Lastly, the kinetic energy of the halfway dark soliton increases exponentially.
In shallow water, solitary waves typically arise as a result of the combined effect of nonlinearity and dispersion. The Boussinesq equation plays a pivotal role in study nonlinear solitary wave due to existing dispersive and nonlinear terms. This study aims to conduct a comprehensive investigation on Boussinesq equation through Lie symmetry method. By determining the complete Lie algebra of infinitesimal generators and constructing one dimensional optimal system of subalgebras, the test equation is transformed to ordinary differential equations (ODEs). The ODEs enable to derive a rich variety of exact solutions, which include bright and dark solitons, double soliton configurations, and many others. To examine the qualitative behavior and structural transitions of these solutions, bifurcation theory is applied, offering a robust framework to study the effects of critical parameters on the dynamics and revealing shifts between distinct solution regimes. Stability is analyzed through bifurcation diagrams and phase portraits, capturing influence of perturbations or parameter variations to evolution of wave structures. Additionally, sensitivity and chaotic analysis are introduced to assess the effect of variations in initial conditions and parameters to persistence and robustness of the derived periodic and quasi-periodic solutions, thereby highlighting critical thresholds and transition points. Furthermore, the adjoint equation and conserved vectors are obtained in connection with the identified symmetries within the framework of the Lagrangian formulation. By synthesizing Lie symmetry reductions, bifurcation and stability analysis, sensitivity examination, and conservation law derivation, this work offers a unified framework for probing the intricate dynamics of the Boussinesq equation, advancing the theoretical understanding and practical applicability of nonlinear wave models.
This study introduces a novel investigation into the entanglement dynamics of two-proton decay in 6Be and 12O, using a three-body model to explore quantum correlations in nuclear systems. For 6Be, we measure entanglement using the von Neumann entropy and observe a decline from 0.70 to 0.35–0.40 within 1 ps due to decoherence driven by spatial separation, proton-proton interactions, and core dynamics. In the heavier 12O, the CHSH indicator reveals strong quantum correlations, reaching 2.282 close to the Tsirelson bound (2√(2)≈ 2.828) , but limited by model simplifications and environmental effects. Through time-dependent simulations with realistic nuclear potentials, we uncover the critical roles of proton-proton interactions and core structure in sustaining entanglement. These findings not only advance our understanding of quantum phenomena in nuclear decay but also address a key gap in connecting nuclear physics with quantum information science, paving the way for future experimental exploration of entanglement in proton-rich nuclei using coincidence measurements.
Spinels possess excellent properties for use in advanced applications. Here in this study, using density functional theory (DFT) calculations, we have studied the structural, electronic and optical properties (dielectric function, electron energy loss, extinction coefficient, reflectivity and refractive index, absorption coefficient, optical conductivity) of spinel compounds of the form MgA2X4 (A = Sc/Y; X = S, Se) under the effect of applied pressure. Interesting physical variations were observed in these materials under the application of pressure. The generalised gradient approximation (GGA) method was performed to figure out structure optimisation. By adopting the modified Becke–Johnson (mBJ) exact exchange technique, electronic and optical properties were computed. The energy band gap is shrunken from 2.9 to 1.6 eV and 0.736 to 0.084 eV for MgA2X4 (A = Sc/Y; X = S, Se) compounds under the effect of pressure. A noticeable variation was seen in the lattice parameters, band gap, electronic and optical properties via exceeding the pressure from 0 to 20 GPa, featuring a prominent absorption coefficient and higher optical conductivity in the visible and UV region, showing greater potential for their use in high-frequency devices. The compounds have the appropriate band gaps for water splitting through redox reactions.
