Novel constructed dynamical analytical solutions and conserved quantities of the new (2+1)-dimensional KdV model describing acoustic wave propagation by Khalique Chaudry Masood, Lephoko Mduduzi Yolane Thabo

“…These solutions exhibit broad applicability across diverse disciplines within nonlinear science and engineering. To provide a deeper understanding of the obtained solutions, we present our findings through visual representations, utilizing three-dimensional, two-dimensional, and density plots. …”
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Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation by Ali R. Ansari, Adil Jhangeer, Beenish, Mudassar Imran, Abdallah M. Talafha

“…Our results highlight the impact of the method on system dynamics and demonstrate its effectiveness in studying solitons and phase behavior in nonlinear models. These findings offer new insights into how the proposed approach can induce significant changes in system dynamics, emphasizing its utility in the analysis of soliton solutions and phase visualizations in various nonlinear models. …”
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Ulam–Hyers Stability of Fractional Difference Equations with Hilfer Derivatives by Marko Kostić, Halis Can Koyuncuoğlu, Jagan Mohan Jonnalagadda

“…This paper investigates the Ulam–Hyers stability of both linear and nonlinear delayed neutral Hilfer fractional difference equations. …”
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Elevated pulse wave velocity as a marker of arterial stiffness and its association with mortality in US adults by Kai Liu, Zhang Lin, Ying Chen, Huashan Hong

“…RCS regression analysis revealed a nonlinear association between ePWV, a marker of arterial stiffness, and all-cause mortality with an inflection point at 8.267 (P for nonlinear = 0.0001), while a positive linear correlation was observed with cardiovascular mortality (P for nonlinear = 0.889). …”
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Application of Array Imaging Algorithms for Water Holdup Measurement in Gas–Water Two-Phase Flow Within Horizontal Wells by Haimin Guo, Ao Li, Yongtuo Sun, Liangliang Yu, Wenfeng Peng, Mingyu Ouyang, Dudu Wang, Yuqing Guo

“…Water holdup imaging provides a valuable means for visualizing the spatial distribution and proportion of gas and water phases within the wellbore. …”
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Advancements in Efficient Underwater Image Restoration Using ETransMapNet for Enhanced Dehazing by C. P. Indumathi, Haya Mesfer Alshahrani, N. A. Natraj, C. H. Sarada Devi

“…ETransMapNet is designed with convolution layers and nonlinear activations to execute four sequential processes: nonlinear regression, local maxima detection, multi-scale decomposition, and convolutional feature extraction. …”
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Research on Fracture Energy Prediction and Size Effect of Concrete Based on Deep Learning with SHAP Interpretability Method by Huiming Wang, Weiqi Zhang, Jie Lin, Shengpin Guo

“…Moreover, owing to the complex nonlinear behavior exhibited by concrete during the fracturing process, existing empirical formulas exhibit restricted precision when forecasting fracture energy. …”
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Interferometric backward third harmonic generation microscopy for axial imaging with accuracy beyond the diffraction limit. by Daaf Sandkuijl, Lukas Kontenis, Nuno M Coelho, Christopher McCulloch, Virginijus Barzda

“…A new nonlinear microscopy technique based on interference of backward-reflected third harmonic generation (I-THG) from multiple interfaces is presented. …”
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Modified Lindstedt-Poincare transformation for fractal resonance approach in vibration 2-DOF heterogeneous system by Yusry O El-Dib, Haifa A Alyousef

“…The study applies a harmonic equivalent linearized approach (HELA) to convert nonlinear equations into linear systems, allowing for the derivation of analytical solutions and extensive numerical comparison. …”
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Investigation Limb darkening for short period AB Andromeda eclipsing binary star by Chiman Ibrahim Hussein Mrs

“…Calculate limb darkening for monochromatic pass bounds, the visual rang i.e. intermediate (uvby) have been calculated and broad bands to the near infrared. …”
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Association of the body roundness index with chronic diarrhea and chronic constipation: findings based on the National Health and Nutrition Examination Survey 2005–2010 data by Yinda Wang, Fei Chen, Binzhong Zhang, Zhengwei Song

“…To assess the relationship between digestive health and the BRI, this study employed weighted logistic regression analysis. To capture and visualize the nuanced interplay between BRI and gastrointestinal patterns, we utilized advanced nonlinear regression methods, specifically restricted cubic spline (RCS) analyses. …”
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VHR Multispectral Satellite Image Classification with Kolmogorov-Arnold Networks for Urban Applications by M. Fawzy, M. Fawzy, Á. Barsi

“…When multispectral data is incorporated, KAN excels by leveraging its ability to model nonlinear relationships, allowing for highly accurate classifications. …”
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A mathematical approach to the role of chemical reactions and temperature-dependent fluid properties on the peristaltic transport of non-Newtonian Ree-Eyring fluid in a nonuniform... by Prathiksha Sanil, Manjunatha Gudekote, Rajashekhar Choudhari, Madhavi M. R., Hanumesh Vaidya, Kerehalli Vinayaka Prasad

“…Solution Methodology A regular perturbation technique is applied to solve the nonlinear equations. MATLAB R2023a is used to visualize the impact of critical parameters like velocity, temperature, concentration, and streamlines under varying physical conditions. …”
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An Algorithm for Reconstructing Radiation Distribution Map in Unknown Environment Based on Mobile Robots by HUO Jian-wen, HU Xu-lin, WANG Jun-ling, GUO Yun-lei

“…The method can deal with complex problems such as small samples, nonlinearity and high dimension, and can quickly draw an environmental radiation distribution map. …”
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Generalized J-integral – mathematical foundation by Kohji Ohtsuka

“…The theory can be numerically calculated and is useful for visualization of shape sensitivities and diagnosis of stress concentrations.…”
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Dynamical Tangles in Third-Order Oscillator with Single Jump Function by Jiří Petržela, Tomas Gotthans, Milan Guzan

“…This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. …”
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Symmetry Analysis and Wave Solutions of Time Fractional Kupershmidt Equation by Shalu Saini, Rajeev Kumar, Kamal Kumar

“…The obtained reduced equation is of fourth order nonlinear ordinary differential equation. To find the wave solutions, F/G-expansion process has been used to obatin different types of solutions of the time-fractional Kuperschmidt equation. …”
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Bilinear form and soltion solutions for (3+1)-dimensional negative-order KdV-CBS equation by Chen Dan

“…It is anticipated that these solutions will not only deepen our understanding of the physical phenomena associated with the equation but also reveal more complex physical behaviors, thereby advancing analytical studies on solutions to other nonlinear partial differential equations.…”
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Relationship between depression and oral microbiome diversity: analysis of NHANES data (2009–2012) by Xichenhui Qiu, Ting Xu, Yiqing Huang, Changning Wei, Lina Wang, Bei Wu

“…Threshold effect analysis was performed to explore potential nonlinear relationships between the observed ASVs and depression. …”
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Selkov’s Dynamic System of Fractional Variable Order with Non-Constant Coefficients by Roman Parovik

“…This article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. …”
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