Pramana最新文献

{"title":"A new perspective for obtaining analytical solitons of the fractional Kaup–Kupershmidt equation","authors":"Francis Tuffour,&nbsp;Benedict Barnes","doi":"10.1007/s12043-026-03177-6","DOIUrl":"10.1007/s12043-026-03177-6","url":null,"abstract":"<div><p>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, <span>(frac{d^{gamma }phi }{dxi ^{gamma }} = p + phi ^2(xi ),)</span> 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 <i>L</i>-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 <i>L</i>-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 <i>L</i>-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.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Soliton dynamics of Boussinesq equation: Lie symmetries, optimal classification, exact solutions, conservation laws, bifurcation structures and sensitivity analysis","authors":"Rajat Kumar,&nbsp;Dig Vijay Tanwar,&nbsp;Satya Jeet Singh","doi":"10.1007/s12043-026-03193-6","DOIUrl":"10.1007/s12043-026-03193-6","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149131985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lie group theoretic method to cylindrical and spherical shock waves in self-gravitating dusty gas with magnetic field","authors":"ARTI Devi,&nbsp;G Nath","doi":"10.1007/s12043-026-03172-x","DOIUrl":"10.1007/s12043-026-03172-x","url":null,"abstract":"<div><p>This study explores self-similar solutions to shock-wave propagation in a self-gravitating, perfectly conducting dusty gas influenced by a magnetic field, using the group-invariance technique. The system of partial differential equations is transformed to a system of ordinary differential equations, which are subsequently solved numerically by using the fourth-order Runge–Kutta scheme implemented in Mathematica. The analysis of physical flow parameters provides insights into the distribution of physical flow variables and the strength of shock waves. A notable advantage of employing the Lie group-theoretic method is that it yields all possible solution cases, unlike other methods, such as similarity solutions using dimensional analysis, which typically address only one case at a time. The findings indicate that increases in the adiabatic exponent, magnetic field strength, and non-idealness parameter of the gas reduce the shock wave strength. Conversely, changing the geometry from cylindrical to spherical, as well as increasing the mass concentration of solid particles or the ratio of solid-particle density to the initial gas density, enhances the shock strength.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Levenberg–Marquardt neural network analysis of MHD bio-convective MgO–Ag hybrid nanofluid flow over a Riga plate with slip and thermophoretic effects","authors":"Hamid Qureshi,&nbsp;Komal Bashir,&nbsp;Alina Latif,&nbsp;Taseer Muhammad","doi":"10.1007/s12043-026-03183-8","DOIUrl":"10.1007/s12043-026-03183-8","url":null,"abstract":"<div><p>The present study examines the fascinating relationship between magnetohydrodynamic (MHD) hybrid nanofluids laden with motile microorganisms and an actuated Riga plate, driven by electromagnetic forces. The novel suspension of magnesium oxide (MgO) and silver (Ag) nanoparticles in water, known as the working fluid, is intended to serve as an intelligent thermal medium that promotes heat and mass transfer. To be realistic, the formulation model incorporates complex yet realistic effects such as flow rate, thermal slip, activation energy, thermophoretic diffusion, and a homogeneous heat source or sink. By similarity, partial differential equations (PDEs) are transformed to a system of ordinary differential equations ODEs and a synthetic dataset is generated numerically, then simulations are processed through a predictive framework, which is an AI-based predictive model, built on the machine learning-based backpropagation mechanism of the neural network, the Levenberg-Marquardt algorithm. The findings indicate that high slip parameters strongly inhibit fluid motion, resulting in a low-strength temperature field and low nanoparticle concentration. It is noteworthy that the AI model shows a prominent level of consistency with the numerical outcomes, proving the strength and precision of the method. This is a collective study in mathematical modeling, computational fluid dynamics, and artificial intelligence that will demystify the multifaceted nature of bio-convective hybrid nanofluids and is a step towards next-generation smart thermal-fluid and energy management systems.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanism of interfacial nanolayer thickness on couple-stress penta-hybrid nanofluids over a stretching sheet for solar thermal applications","authors":"Varsha Kohli,&nbsp;Chandrakanta Parida,&nbsp;Saheed Ojo Akindeinde,&nbsp;Ganeswar Mahanta,&nbsp;Sachin Shaw","doi":"10.1007/s12043-026-03189-2","DOIUrl":"10.1007/s12043-026-03189-2","url":null,"abstract":"<div><p>The impact of interfacial nanolayer thickness is critical in modeling heat transfer in nanofluids, especially when nanoparticle sizes are below 10 nm. These nanolayers, which naturally form around nanoparticles, significantly enhance thermal conductivity and heat flux, making them essential in applications like biomedical cooling, microfluidics, and drug delivery. This study examines the unsteady boundary-layer flow of a Boussinesq couple-stress fluid through a Darcy–Forchheimer porous medium, utilizing a penta-hybrid nanofluid while explicitly accounting for nanolayer effects. Modified Maxwell-type models are used to account for nanolayer-to-radius ratios, thereby improving the estimation of effective thermophysical properties for all five nanoparticles. The model includes the effects of thermal radiation, Joule heating, viscous dissipation, velocity slip, and magnetic fields. Similarity transformations reduce the governing equations to ordinary differential form, solved numerically via the shooting method with a fourth-order Runge–Kutta scheme. The framework is applicable to solar thermal collectors with flexible absorbers exposed to radiative and electromagnetic loading. Results show that velocity decreases with increasing Casson number, couple stress, porosity, and suction, whereas stretching enhances flow. Temperature increases with radiation and Biot number but decreases with stronger heat generation. Penta-hybrid nanofluid consistently outperforms simpler nanofluids in both skin friction and heat transfer efficiency, validating its thermal superiority.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entanglement and fidelity in hydrogen electron–proton spins amid magnetic fields and decoherence","authors":"SMAIL BOUGOUFFA,&nbsp;KAMAL BERRADA","doi":"10.1007/s12043-026-03203-7","DOIUrl":"10.1007/s12043-026-03203-7","url":null,"abstract":"<div><p>We explore the time evolution of entanglement and fidelity in the electron–proton spin system of a hydrogen atom under the influence of external magnetic fields and Markovian dephasing noise. The hydrogen atom serves as a paradigmatic two-qubit system, in which hyperfine coupling generates intrinsic spin correlations, modulated by Zeeman splitting, which introduces field-dependent energy shifts and controls spin evolution. We consider the open-system dynamics using the Lindblad equation, incorporating local dephasing processes arising from magnetic-field fluctuations that act independently on the electron and proton spins while preserving population probabilities. Bipartite quantum correlations are quantified via the concurrence and Uhlmann fidelity, which measures the overlap between evolving states and reference preparations. Our analysis elucidates the interplay among hyperfine interactions, Zeeman effects, and environmental decoherence, revealing regimes where entanglement decays rapidly due to noise sensitivity, in contrast to greater resilience in fidelity measures. Time-dependent behaviors highlight field-induced enhancements or suppressions of correlations.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dromion solutions of ({mathbf{(2}}{boldsymbol{+}}{mathbf{1)}})-dimensional breaking equation via generalized Riccati equation method","authors":"S-F Wang","doi":"10.1007/s12043-026-03178-5","DOIUrl":"10.1007/s12043-026-03178-5","url":null,"abstract":"<div><p>Three variable separation solutions of a (2<span>(+)</span>1)-dimensional breaking equation are derived by using the generalized Riccati equation method. Then, using the soliton solutions and appropriate auxiliary functions, two dromion lattices and multi-dromion soliton solutions are constructed, and the collision or interaction phenomena between two multi-dromions are discussed. In addition, the fractal structures for the dromion solution of the proposed breaking equation are revealed.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat transfer of Casson fluid flow through atherosclerotic artery","authors":"Md Asif Ikbal","doi":"10.1007/s12043-026-03180-x","DOIUrl":"10.1007/s12043-026-03180-x","url":null,"abstract":"<div><p>The present study emphasizes the computational investigation of heat transfer through the atherosclerotic artery. Blood is considered incompressible, non-Newtonian, and fully developed Casson fluid. The Casson fluid model, with its yield-stress behavior is used to represent rheological properties, especially in regions of high shear near arterial constrictions. Geometrically, the computational domain is constructed from the patient-specific stenotic artery. The momentum equations along with appropriate boundary conditions are solved numerically using the Marker and Cell (MAC) method. Necessary numerical stability conditions have been integrated into the algorithm to enhance the accuracy of the computed results. Quantitative analysis has been studied, including a detailed profile of the temperature distribution for different parameters. The results indicate that the temperature of the blood increases as the blood moves toward the downstream in the artery. The effect of Reynolds number (<i>Re</i>) and Prandtl number (<i>Pr</i>) on the distribution of blood temperature is evident in all cases.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical solutions of the fractional TOV equations for relativistic isothermal spheres","authors":"M. S. Aboueisha,&nbsp;M. I. Nouh,&nbsp;Emad A.-B. Abdel-Salam,&nbsp;Mona M. Foda","doi":"10.1007/s12043-026-03153-0","DOIUrl":"10.1007/s12043-026-03153-0","url":null,"abstract":"<div><p>The relativistic isothermal gas sphere provides a valuable model for investigating stellar properties, though its applicability becomes limited in the regime of compact stars where relativistic corrections are essential. In this work, we extend the classical Tolman–Oppenheimer–Volkoff (TOV) formulation to the fractional domain by employing the modified Riemann–Liouville (mRL) derivative, thereby constructing the fractional TOV (FTOVI) equations. An analytical solution is obtained via a series expansion accelerated by Euler–Abel transformations and Padé approximations, ensuring convergence up to the stellar surface. Our analysis shows that decreasing the fractional parameter α below unity systematically reduces both the mass and radius of the sphere, while enhancing central density. The Emden function exhibits small but persistent irregular modulations for <i>α</i> &lt; 1, even after resummation, indicating the intrinsic nonlocal effects of the mRL operator. For relativistic parameters <i>σ</i> = 0.1−0.3, the mass–radius relation demonstrates a maximum stable configuration at compactness ratios consistent with neutron-star analogs. In particular, the central density–mass curve reveals a well-defined maximum mass beyond which instability sets in; fractional models predict lower maximum masses than the integer-order case. The constructed configurations satisfy the criteria of regularity, causality, and standard energy conditions, and they remain dynamically stable according to the adiabatic index criteria. The FTOVI mass–radius curves are directly compared with 21 observed neutron stars from X-ray, NICER, and gravitational-wave data. It concludes that <span>(alpha =1)</span> fits the most massive stars, while mildly fractional models (<span>(alpha approx 0.95)</span>) match the bulk of typical systems, showing observational consistency. These results highlight both the predictive capacity and the richer structural behavior of the mRL-based FTOV framework, offering a fractional extension of classical relativistic models with potential relevance to realistic compact stars.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Entanglement dynamics in two-proton decay of 12O and 6Be","authors":"Hassan Khalili,&nbsp;Mahdi Azad Marzabadi","doi":"10.1007/s12043-026-03145-0","DOIUrl":"10.1007/s12043-026-03145-0","url":null,"abstract":"<div><p>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 <span>((2sqrt 2 approx 2.828))</span>, 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.</p></div>","PeriodicalId":743,"journal":{"name":"Pramana","volume":"100 4","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}