Approximate Analytic Solution for the KdV and Burger Equations with the Homotopy Analysis Method by Mojtaba Nazari, Faisal Salah, Zainal Abdul Aziz, Merbakhsh Nilashi

“…The homotopy analysis method (HAM) is an analytic technique which provides us with a new way to obtain series solutions of such nonlinear problems. HAM contains the auxiliary parameter ħ, which provides us with a straightforward way to adjust and control the convergence region of the series solution. …”
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Description of Dispersive Wave Emission and Supercontinuum Generation in Silicon Waveguides Using Split-Step Fourier and Runge-Kutta Integration Methods by Xuefeng Li

“…Based on solving numerically the generalized nonlinear Schrödinger equation describing the propagation of high order femtosecond soliton in silicon waveguide under certain parametric conditions by the split-step Fourier and Runge-Kutta integration methods, dispersive wave emission and supercontinuum generation in silicon waveguides are numerically investigated by propagating femtosecond solitons. …”
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Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation by Xiaolian Ai, Lingyu Jiang, Ting Yi

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Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation by Bo Ren

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On the Hadamard Well-Posedness of Generalized Mixed Variational Inequalities in Banach Spaces by Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, Hui-Ying Hu, Long He, Yun-Ling Cui

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Energy transfer aspects of chemically reactive Casson fluid between a conical gap of cone-disk system with multiple rotations by M. Qamar, M. Khan, A.S. Alqahtani, M.Y. Malik

“…The physical characteristics of nonlinear PDEs are converted into nonlinear coupled ODEs utilizing the right similarity variables. …”
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Data-Driven Bearing Fault Diagnosis of Microgrid Network Power Device Based on a Stacked Denoising Autoencoder in Deep Learning and Clustering by Fast Search without Data Labels by Fan Xu, Xin Shu, Xin Li, Xiaodi Zhang

“…The SDAE can extract the representative degradation information adaptively from the original data through several nonlinear hidden layers automatically and approximate complicated nonlinear functions with a small reconstruction error. …”
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Evidence from NHANES 2011–2014: a correlation between the weight-adjusted-waist index and cognitive abilities in the United States by Chan Zhao, Xintian Xu, Chunyan Hao

“…Furthermore, we performed a smoothenable curve fitting between WWI and cognitive function scores, resulting in a nonlinear connection and a threshold saturation effect. …”
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Associations between phenol and paraben exposure and the risk of developing breast cancer in adult women: a cross-sectional study by Yao Xiong, Zhiyu Li, Xiong Xiong, Zixuan Luo, Kaixin Zhong, Jiawei Hu, Shengrong Sun, Chuang Chen

“…The results from the weighted multivariable regression models indicated that exposure to elevated concentrations of TRS increased the risk of developing BC by 2.33 (Q2: 95% CI = 1.45–3.75, p < 0.001) and 1.94 times (Q3: 95% CI = 1.21–3.09, p = 0.006), respectively. The nonlinear association between TRS concentrations and the risk of developing BC was statistically significant (P nonlinear = 0.007), with the restricted cubic splines (RCS) curve exhibiting an inverted U shape. …”
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Effect of Walking Speeds on Complexity of Plantar Pressure Patterns by Ben-Yi Liau, Fu-Lien Wu, Yameng Li, Chi-Wen Lung, Ayman A. Mohamed, Yih-Kuen Jan

“…Current methods used to analyze plantar pressure patterns are linear and ignore nonlinear features. The purpose of this study was to analyze the complexity of plantar pressure images after walking at various speeds using nonlinear bidimensional multiscale entropy (MSE2D). …”
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Individual and joint effects of exposure to multiple organophosphate esters and the risk of depression in adults: Differences in sex, age, and physical activity by Qingmiao Wei, Jiyun Wei, Jun Liang

“…In the BKMR, a positive association was noted between OPE mixtures and depression scores, and a U-shaped nonlinear association was noted between OPE mixtures and the risk of depression. …”
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Visible light-responsive hydrogels for cellular dynamics and spatiotemporal viscoelastic regulation by Yan Lu, Cheng Chen, Hangyu Li, Peng Zhao, Yuanfeng Zhao, Bohan Li, Wei Zhou, Gaofeng Fan, Dongshi Guan, Yijun Zheng

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Management of Uncertainty by Statistical Process Control and a Genetic Tuned Fuzzy System by Stephan Birle, Mohamed Ahmed Hussein, Thomas Becker

“…In general, they are characterized by highly nonlinear dynamics and uncertainties that make it difficult to control these processes by the use of traditional control techniques. …”
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Relationship of METS-IR with cardiometabolic multimorbidity in China: a nationwide longitudinal cohort study by Chunyan Zhou, Yanyu Zhang, Xiaoyi Liu, Chenyu He, Shiyang Li, Shiyang Li

“…RCS analysis revealed a significant nonlinear association between METS-IR and CMM (nonlinear p &lt; 0.05). …”
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Membrane Transport of Nonelectrolyte Solutions in Concentration Polarization Conditions: Hr Form of the Kedem–Katchalsky–Peusner Equations by Kornelia M. Batko, Andrzej Ślęzak

“…The coefficients ψ12, ψ13, ψ22 = ψ23, ψ32 = ψ33, and ψdet depend nonlinearly on solution concentration and for C¯1 ≈ 9.24 mol m−3 are equal to zero. …”
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Study on the evolution law of the ‘Butterfly-type’ plastic zone in the surrounding rock of deep dynamic pressure roadway by Yiwen Liang, Jianqiang Jin, Wenhua Zha, Tao Xu, Wenbo Cheng

“…Based on the Hoek–Brown strength criterion, the unified strength theory is modified and the nonlinear unified strength theory of rock is established by comprehensively considering the intermediate principal stress, rock properties and rock structure. …”
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Association between a body shape index and colorectal cancer in US population: a cross-sectional study based on NHANES by Hui Liu, Jialu Kang, Wei Liu, Yongqing Shen

“…RCS analysis indicated a nonlinear correlation between ABSI and CRC (P for nonlinear = 0.030). …”
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Measuring effective indicators for waste disposal in order to assess the sustainable environment: application of fuzzy approach by Mohammad Hossein Kabgani

“…Also, the technical contribution of this article is presented by combining fuzzy logic and Nonlinear mathematical programming.…”
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Spline approximation of multivalued functions in linear structures routing by D. A. Karpov, V. I. Struchenkov

“…At the second stage, nonlinear programming is used. In this case, it is possible to analytically calculate the derivatives of the objective function with respect to the spline parameters in the absence of its analytical expression through these parameters.Results. …”
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Hybrid Prophet-NAR Model for Short-Term Electricity Load Forecasting by Winita Sulandari, Yudho Yudhanto, Etik Zukhronah, Isnandar Slamet, Hilman Ferdinandus Pardede, Paulo Canas Rodrigues, Muhammad Hisyam Lee

“…Traditional models like SARIMA and Singular Spectrum Analysis (SSA) have been widely used but often need to capture complex nonlinear patterns and deal with data uncertainties. …”
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