International Journal of Modern Physics B

Under investigation in this paper is the long-wave-short-wave resonance system, which can describe a variety of nonlinear wave phenomena such as the two-dimensional packets of capillary-gravity waves in hydrodynamics and the optical-terahertz waves. The intended aim is carried out via considering a traveling wave reduction, adopting a modified version of the Jacobi elliptic expansion method and employing the Weierstrass elliptic function method to derive such analytic solutions as the bright and dark soliton solutions, periodic solutions, trigonometric-function and elliptic-function solutions in fluid mechanics.

A mathematical model for nonlinear quadratic convection with non-Fourier heat flux in coating boundary layer flow of a Maxwell viscoelastic fluid is presented. Nonlinear quadratic thermal radiation and heat source/ sink effects are also considered. The transformations of Lie symmetry are employed. The resultant nonlinear differential equations with defined boundary conditions are numerically solved using the spectral relaxation technique (SRM), a robust computational methodology. Graphical visualization of the velocity and temperature profiles is included for a range of different emerging parameters. For skin friction and the Nusselt number, numerical data are also provided. There is a very strong correlation between the outcomes of this study and those published in the literature. Higher values of the nonlinear thermal radiation, mixed convection, thermal conductivity, nonlinear convection and heat source/ generation parameters increase temperature as well as the thickness of the thermal boundary layer. However, a higher Prandtl number, thermal relaxation parameter and heat sink/ absorption parameter all reduce temperature. Deborah number causes velocity to be raised (and momentum boundary layer thickness to be lowered), whereas raising nonlinear mixed convection parameter causes velocity to be decreased (and momentum boundary layer thickness to be increased), and a velocity overshoot is calculated. The models are applicable to simulations of high-temperature polymeric coatings in material processing.

In this study, the integrability conditions on mixed derivative nonlinear Schrödinger equations are the focus of this work. A. Rangwala mathematically defined these effects and dubbed this form the Rangwala–Rao equation (${ℛ}{ℛ}$) in 1990. Using innovative soliton wave solutions and their interactions, we hope to better understand how dispersion affects the electric field and pulse propagation in optical fibers. Generalized Khater (GKhat.) provides unique solitary wave solutions to the ${ℛ}{ℛ}$ problem. The pulses’ dynamical behavior through optical fibers is seen in these numerical simulations. The originality of the paper’s conclusions may be seen by contrasting our findings with those of other researchers.

We present the modified simple equation method for solving nonlinear fractional-order partial differential equations (fPDEs). With the presented method, some important fPDEs are solved. We used conformable derivatives to solve these equations. The solutions obtained are both hyperbolic and trigonometric function solutions. Most of these solutions are new solutions not found in the literature.

In this paper, we study the statistical complexity in the Bose–Hubbard model using two statistical quantifiers, namely, the LMC and SDL measures. We discuss the effect of temperature, magnetic field, time and interactions on complexity. Our analysis unveils the rich interplay between entropy and disequilibrium in this model.

Pr${}_{0.7}$Sr${}_{0.3}$MnO₃ thin films were grown epitaxially on SrTiO₃ and LaAlO₃ substrates by pulse laser deposition. X-ray diffraction spectra obtained on these films revealed good crystallinity and epitaxy. It was found that the oxygen deficiency and in-plane strain may affect the transport behavior and phase transition near Curie temperature in these Pr${}_{0.7}$Sr${}_{0.3}$MnO₃ films. Also, the resistance and metal-insulator phase transition could be modulated significantly by the applied electric currents. The reduction ratio of the peak resistance reached −38% for a bias current $I=500\mu$A, demonstrating a remarkable electroresistance effect. The results are interpreted based on the spatial inhomogeneity related to the coexisted multi-phases with different electronic and magnetic properties.

In this paper, we investigate multiple soliton interactions and other solitary wave solutions (SWS) for a perturbed nonlinear Schrödinger equation (NLSE) with negative index material having quadratic-cubic nonlinearity (NLSE-QCN). Due to its high order dispersion term, this model yields sub-picosecond impulses useful in mode-locked ring lasers. Hirota bilinear method (HBM) will be used to study soliton interaction. By controlling the parameters, we will obtain $S$, $V$, parabolic and anti-parabolic, butterfly, bright and dark shaped solitons. On the other hand, we will obtain some other solitary wave solutions with the help of Sine-Gordon expansion (SGE) scheme.

This paper examines the influence of magnetized Casson nanofluid flow and heat transport phenomena towards a boundary layer flow over a nonlinear stretchable surface. The characteristics of the nanofluid are illustrated by considering Brownian motion and thermophoresis effects due to which the fluid is electrically conducting. The nonlinear Casson model is very useful to describe the fluid behavior and the flow curves of suspensions of pigments in lithographic varnishes intended for the preparation of printing inks. A uniform magnetic field, along with suction and chemical reaction are taken into account. Similarity transformations are employed to convert the PDEs into ODEs, and then solved numerically (Bvp4c) using MATLAB. This scheme consists of a finite difference scheme that implements three-stage Lobatto IIIa collocation formula which provides continuous solution upto fifth-order accuracy. Excellent correctness of the present results has been acquired which is compared with the previous one. The outcomes of various parameters on heat transfer rate, skin friction coefficient, nanoparticle concentration, Sherwood number, velocity and temperature profiles are demonstrated via tabular forms and pictorially. The most important fact is that an increase in the thermophoresis parameter, radiation and magnetic parameter boosts up the fluid temperature, resulting in an improvement in the thermal boundary layer.

Among several aspects, the one contributing towards the difficulty of groundwater quality evaluation is the large diversity of contamination sources. As contaminants comprising various compounds move from the soil to the water table, they will travel through several hydrologic zones. In constant unidirectional flow fields, a mathematical study of simultaneous adsorption and dispersion of a solute inside homogeneous and isotropic permeable media is described. The solute is adsorbed at a rate proportionate to its concentration in the dispersion systems, which are susceptible to input concentrations that fluctuate exponentially with time. The advection–dispersion equation (ADE) was solved numerically in this work to analyze the pollutants transport bearing in mind the coefficient of distribution and permeability by considering pollutant input concentrations. The solution is derived using the Laplace transform and Duhamel’s theorem with moving coordinates. For specified medium and fluid characteristics, mathematical methods are created to forecast the concentration of pollutants in adsorbing porous media.

In this paper, we construct multiple soliton solutions of a time-dependent variable-coefficient Korteweg–de Vries equation in the form of bright, dark and singular soliton solutions. Furthermore, the periodic solutions are derived. These will be achieved via the aid of solitary wave ansatz methods. In addition, other exact solutions of a time-dependent variable-coefficient Korteweg–de Vries equation are attained using symmetry reductions. In one special case, the power series method is employed to derive a solution of the aforesaid equation. We also examine the conservation laws of the aforementioned equation using the variational approach. A brief physical representation of the derived conserved vectors will be conversed.