Exact Soliton Solutions to the Variable-Coefficient Korteweg–de Vries System with Cubic–Quintic Nonlinearity by Hongcai Ma, Xinru Qi, Aiping Deng

“…Under the help of the wave ansatz method, we obtain the exact soliton solutions to the variable-coefficient KdV system, such as the dark and bright soliton solutions, Tangent function solution, Secant function solution, and Cosine function solution. …”
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Propagation Properties of Laguerre–Gaussian Beams with Three Variable Coefficient Modulations in the Fractional Schrödinger Equation by Xinru Hao, Yong Liang, Min Zou, Bin Zhong, Chao Tan

“…This article investigates the transmission characteristics of Laguerre–Gaussian (LG) beams under cosine modulation, power function modulation and linear modulation based on the variable coefficient fractional Schrödinger equation (FSE), respectively. …”
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Calculation of heating laminar fluid flow with variable heat transfer coefficient on the surface of circular channel by U. V. Vidin, V. S. Zlobin, R. V. Kazakov

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Variable step-size LMS algorithm with hybrid weight coefficients based on the Rayleigh distribution curve by CHEN Dongwei, LIU Weidong, ZHANG Mingyi, JIN Mengzhe, FANG Qingyuan

“…The impact of the new variable step function parameters <italic>α</italic>, <italic>β</italic>, <italic>γ</italic> and the hybrid filter weight coefficient <italic>W</italic>(<italic>n</italic>) on the proposed algorithm performance and interference suppression analysis were discussed in detail. …”
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Lie Group Classification of a Class of Variable Coefficient Boiti–Leon–Manna–Pempinelli Equations by Christodoulos Sophocleous

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Novel Nonlinear Dynamical Solutions to the (2 + 1)‐Dimensional Variable Coefficients Equation Arise in Oceanography by Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, Shams Forruque Ahmed

“…The assistance of the Hirota bilinear method secures different forms of multiple solitons and M‐lump waves, such as one‐, two‐, and three‐soliton, by using different functions of variable coefficients. Moreover, the long‐wave technique is under consideration when analyzing hybrid solutions, namely mixed soliton‐lump, two‐soliton‐lump, and soliton‐two‐lump solutions. …”
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Predicting filtration coefficient and formation damage coefficient for particle flow in porous media using machine learning by Xuejia Du, George K. Wong

“…The clogging of porous media with solid particle suspension flow is modeled using two empirical parameters of filtration coefficient (λ) and formation damage coefficient (β). …”
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Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators by Yuye Zou, Chengxin Wu

“…In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. …”
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Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients by Zhao Li, Peng Li, Tianyong Han

“…Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.…”
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Series Solution Method Used to Solve Linear Caputo Fractional Initial Value Problems with Variable Coefficients by Aghalaya S Vatsala, Govinda Pageni

“…Computing the solution of the linear Caputo fractional differential equation with variable coefficients cannot be obtained in closed form as in the integer-order case. …”
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Approximation of an Optimal BV -Control Problem in the Coefficient for the p(x)-Laplace Equation by Ismail Aydin, Peter Kogut

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On empirical Bayes estimation of multivariate regression coefficient by R. J. Karunamuni, L. Wei

“…We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y=Xβ+ε, where Y is an m-vector of observations, X is a known m×k matrix, β is an unknown k-vector, and ε is an m-vector of unobservable random variables. …”
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Local RBF-FD-Based Mesh-free Scheme for Singularly Perturbed Convection-Diffusion-Reaction Models with Variable Coefficients by Ram Jiwari, Sukhveer Singh, Paramjeet Singh

“…This work analyze singularly perturbed convection-diffusion-reaction (CDR) models with two parameters and variable coefficients by developing a mesh-free scheme based on local radial basis function-finite difference (LRBF-FD) approximation. …”
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Inverse Scattering Integrability and Fractional Soliton Solutions of a Variable-Coefficient Fractional-Order KdV-Type Equation by Sheng Zhang, Hongwei Li, Bo Xu

“…However, the solved fNLEEs are all constant-coefficient models. In this study, we establish a fractional-order KdV (fKdV)-type equation with variable coefficients and show that the IST is capable of solving the variable-coefficient fKdV (vcfKdV)-type equation. …”
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Dissipation Scaling with a Variable <i>C_ϵ</i> Coefficient in the Stable Atmospheric Boundary Layer by Marta Wacławczyk, Jackson Nzotungishaka, Paweł Jędrejko, Joydeep Sarkar, Szymon P. Malinowski

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Solitons, Lumps, Breathers, and Interaction Phenomena for a (2+1)-Dimensional Variable-Coefficient Extended Shallow-Water Wave Equation by Tianwei Qiu, Zhen Wang, Xiangyu Yang, Guangmei Wei, Fangsen Cui

“…In this paper, soliton solutions, lump solutions, breather solutions, and lump-solitary wave solutions of a (2+1)-dimensional variable-coefficient extended shallow-water wave (vc-eSWW) equation are obtained based on its bilinear form. …”
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Magnetic Deflection Coefficient Investigation for Low Energy Particles by Baghdad Science Journal

“…The results showed had been tabulated and graphically represented as functions of their variables. These results a satisfactory agreement between experimental values and theoretical data given in the literature showed.…”
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Investigating fluctuation varieties in the propagation of the perturbed KdV equation with time-dependent perturbation coefficient by Marwan Alquran

“…By assigning various functional forms such as periodic, polynomial, and decaying exponential, to the proposed time-dependent coefficient, novel solitary wave patterns of types like-breather, regular(singular)-bell shaped, and periodic solutions are emerged with fluctuations. …”
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Distribution Formulae of the Solute in Transport of Advection-Dispersion of Air Pollution for Different Wind Velocities and Dispersion Coefficients by Frederic Ayant, Hemant Kumar, M Pathan

“…In this paper, we obtain certain distribution formulae of the solute in transport of the typical advection-dispersion of air pollution through separation in two-dimensional space variables by introducing different wind velocities and dispersion coefficients. …”
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A Case Study on the Influence of Friction Coefficient and Rotational Speed on Transient Thermoelastic Response of FGM Rotating Cylinder by Reza Koohi Faegh Dehkourdi, Mostafa Omidi Bidgoli, Mohammad Hosseini

“…The material property is assumed to be variable along radius according to a volume fraction distribution. …”
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