Surya Sen Mahavidyalaya

This article demonstrates different aspects of wave dynamics of a nonautonomous multilinear-type ZK equation. The multi-solitons, positons, and breather solutions for the system, along with their interactions, are constructed using Hirota’s bilinear method. These solutions capture the nonlinear wave interactions effectively, enabling the study of complex solution dynamics such as collisions and resonant interactions in a mathematically tractable way. The dynamical system of the said multilinear equation analyzed through phase portrait techniques, reveals intricate behavior near equilibrium points. This analysis identifies solution types such as super nonlinear orbits, periodic orbits, and solitons, highlighting their roles in the system’s stability and transitions. The system also exhibits singular solutions under certain conditions. The new finding here is the formation of supernonlinear orbits during different intermittency stages playing an important role in the system’s dynamics–these orbits can generate chaotic structures or stabilize the system, preventing it from becoming chaotic or turbulent. These complex trajectories–encompassing periodic, quasiperiodic, and supernonlinear orbits–are investigated across both the autonomous and nonautonomous regimes of the system. By leveraging analytical solutions alongside phase portrait analysis, this study critically evaluates how external driving forces and damping influence various wave structures, including solitons, breathers, and periodic configurations. This study underscores the importance of these nonlinear orbits in shaping the system’s evolution, contributing to the broader understanding of chaotic and stable regimes in nonlinear dynamical systems.

The paper presents in-depth studies of the dielectric properties and conduction dynamics of Dy-doped CaBaFe4O7 which is a recently characterized magnetoelectric material with strong potentials for technological applications as it shows a near-room-temperature ferrimagnetic transition along with strong ferrimagnetic moment, and gigantic electric polarization change. This work demonstrates the direct correlation of the dielectric and electrical transport properties of Ca1-xDyxBaFe4O7 (x = 0, 0.01, 0.03, and 0.05) with structural distortion through various dc, ac conduction, high-energy x-ray diffraction studies, and modeling of the data. CaBaFe4O7 has a unique structure characterized by alternate stacking of FeO4 tetrahedra in triangular and kagom & eacute; layers. Large structural distortion, competing magnetic interactions, exchange striction effects, and possible charge ordering are expected to play a major role in the dielectric and electrical properties of the material. We report observation of short-range polaron hopping conduction mechanism in the low-temperature regime and signature of large polaronic nature of charge carriers. Modeling of the electric modulus using Havriliak-Negami equation points out both distribution and cooperativeness in the polaron dynamics which can be correlated to the interplay of structural distortion, and the background electric field due to the polar nature of the materials. The Havriliak-Negami parameters closely follow orthorhombic distortion of the structures.

This article demonstrates the characteristic of integrability of the nonautonomous KP-mKP equation through Painlevé analysis, bilinear Bäcklund and lax pairs. The nonautonomous KP-mKP equation is converted into the Bell polynomial from which bilinear Bäcklund is constructed and lax pair of the said equation is generated. Further, multi-solitons, smooth positon, breather, and their interaction are fabricated using Hirota’s bilinear approach. Besides, a qualitative analysis of the nonautonomous KP-mKP equation using bifurcation theory is carried out. The deformation of the periodic to quasiperiodic orbit signifying instability of the said system due to damping is observed. Additionally, the external periodic force perturbs the nonautonomous system’s low- and high-energy orbits, resulting in a chaotic structure via the path of intermittency, implying the presence of turbulent flow.

Kalb–Ramond gravity is expected to show the signatures of the low energy limit of the Lorentz violating extension of the standard model of particle physics. To understand the theory further, we study the circular geodesics belonging to a class of exact solutions [found recently by Lessa, Silva, Maluf, Almeida (LSMA)] by posing them as a Hamiltonian dynamical autonomous system. The analysis on the phase space for relevant values of the Lorentz violating parameters reveals for the first time a wealth of novel information that include prediction of homoclinic orbits, saddle points, separatrices that are not available from the conventional analysis. Their image on the actual physical space is discussed.

The fascinating physical characteristics of the 114-cobaltate, CaBaCo4O7, like alternate stacking of two-dimensional layers of CoO4 tetrahedra in triangular and kagome ' patterns, geometrical frustration, and magnetoelectric coupling have attracted several studies in the magneto-structural and dielectric sectors. But the study of electrical conduction dynamics remains practically unknown. Here we have presented dc conduction studies and ac dielectric spectroscopy intending to un-derstand the charge conduction and charge carrier relaxation dynamics of CaBaCo4O7, along with two chemically substituted derivatives - CaBaCo3.96Cr0.04O7 and CaBaCo3.96Ni0.04O7, of impurity level (1%) substitutions. We observe that dc conduction at low temperatures is mediated by variable range polaron hopping, while the ac conduction study points out small-polaron-tunneling across strongly localized states. Electric modulus obeys the Havriliak-Negami equation, with parameters alpha and gamma significantly less than unity, indicating strong distribution in relaxation times; and its non-exponential nature, pointing out the cooperative motion of charge carriers. Imaginary electric modulus is not scaled to a single master curve for the three samples, signifying differences in charge relaxation dynamics.