Application of the Natural Decomposition Method to Strongly Coupled Partial Differential Equations: The Gray-Scott Model. by Nsingwire, Godwin

“…This study investigated the application of the natural decomposition method for solving the Gray-Scott reaction-diffusion model, which is known for its complex nonlinearities and strong coupling between chemical species. …”
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Solutions of Conformable Fractional-Order SIR Epidemic Model by Atimad Harir, Said Malliani, Lalla Saadia Chandli

“…These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. …”
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The Improved Generalized tanh-coth Method Applied to Sixth-Order Solitary Wave Equation by M. Torvattanabun, J. Simmapim, D. Saennuad, T. Somaumchan

“…The improved generalized tanh-coth method is used in nonlinear sixth-order solitary wave equation. This method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. …”
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Existence Analysis of Multi-Point Boundary Value Problems with Riesz-Caputo Fractional Derivatives by Takieddine Zeghida, Rabah Khaldi, Assia Guezane-Lakoud

“…This paper explores the study of a specific category of nonlinear multi-point boundary value problems (BVPs) associated with Riesz-Caputo fractional differential equations and integral boundary conditions. …”
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Symmetry Breaking Soliton, Breather, and Lump Solutions of a Nonlocal Kadomtsev–Petviashvili System by Hong-Yu Wu, Jin-Xi Fei, Zheng-Yi Ma, Jun-Chao Chen, Wen-Xiu Ma

“…The Kadomtsev–Petviashvili equation is one of the well-studied models of nonlinear waves in dispersive media and in multicomponent plasmas. …”
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FSE-RBFNN-Based AILC of Finite Time Complete Tracking for a Class of Time-Varying NPNL Systems with Initial State Errors by Chunli Zhang, Lei Yan, Yangjie Gao

“…The paper proposed an adaptive iterative learning control (AILC) strategy for the unmatched uncertain time-varying nonparameterized nonlinear systems (NPNL systems). Addressing the difficulty of nonlinear parameterization terms in system models, a new function approximator (FSE-RBFNN) which is combined with radial basis function neural network (RBFNN) and Fourier series expansion (FSE) is introduced to model each time-varying nonlinear parameterization function. …”
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Association between Ambient Illumination and Cognitive Impairment: A Population-Based Study of Older by Tieyi Shi, Baozhong Chen

“…Smooth curve fitting showed that the correlation was nonlinear, with an inflection point at 1.22. Conclusions. …”
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Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics by Imran Siddique, Arshad M. Mirza, Kausar Shahzadi, M. Ali Akbar, Fahd Jarad

“…The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.…”
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The Size Effect and Microstructure Changes of Granite after Heat Treatment by Zhongping Guo, Jian Li, Yongqi Song, Chengqian He, Fuyu Zhang

“…High temperature can change the mechanical properties of granite, with significant nonlinear characteristics, and at the same time change its microstructure. …”
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Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order by A. Kazemi Nasab, A. Kılıçman, Z. Pashazadeh Atabakan, S. Abbasbandy

“…A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. …”
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New Solutions of Elastic Waves in an Elastic Rod under Finite Deformation by Peng Guo, Xiang Wu, Liangbi Wang

“…The nonlinear wave equation of an elastic rod under finite deformation is solved by the extended mapping method. …”
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Robust and Arbitrary Pole Placement using Static Output Feedback by El Faiz Samira, Guerbaoui Mohammed, Ed-Dahhak Abdelali, Lachhab Abdeslam

“…The robust and arbitrary pole placement problem is formulated as a nonlinear and non-convex programming problem with a nonlinear constraint on matrix functions as well as a linear constraint. …”
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Fluid-Induced Vibration Elimination of a Rotor/Seal System with the Dynamic Vibration Absorber by Qi Xu, Junkai Niu, Hongliang Yao, Lichao Zhao, Bangchun Wen

“…The simplified rotor model with the absorber is established, and the Muszynska fluid force model is employed for the nonlinear seal force. The numerical method is used for the solutions of the nonlinear differential equations. …”
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High-Accuracy Surface Profile Measurement Based on the Vortex Phase-Shifting Interferometry by Donge Zhao, Chaozheng Jia, Yayun Ma, Xuefeng Yang, Bin Zhang, Wenbo Chu

“…The results show that nonlinear phase modulation has a great impact on the measurement. …”
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The Characteristics of Seismic Response on Hard Interlayer Sites by Jie Su, Zhenghua Zhou, You Zhou, Xiaojun Li, Qing Dong, Yafei Wang, Yuping Li, Liu Chen

“…With the increase of hard interlayer thickness, the site nonlinear effect on seismic responses decreased. Under the same thickness of the hard interlayer, the nonlinear effect of the site was strengthened with the higher input peak acceleration. …”
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Instantaneous Frequency Identification Using Adaptive Linear Chirplet Transform and Matching Pursuit by Chang Xu, Cong Wang, Jingbo Gao

“…The result shows that it will significantly increase the accuracy of nonlinear frequency trajectory identification.…”
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Experimental Validation of Numerical Model for Bi-Tilt-Isolator by Ming-Hsiang Shih, Wen-Pei Sung, Chia-Yu Ho

“…Sliding force, friction force, and impulse force are caused in the slanting process of BTI, nonlinear behavior. A nonlinear mathematical model is derived based on the sliding upwards, sliding downwards, and transition stages. …”
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Exact Solutions to a Generalized Bogoyavlensky-Konopelchenko Equation via Maple Symbolic Computations by Shou-Ting Chen, Wen-Xiu Ma

“…We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. …”
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Analytical Method in Solving Flow of Viscoelastic Fluid in a Porous Converging Channel by M. Esmaeilpour, Naeem Roshan, Negar Roshan, D. D. Ganji

“…The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.…”
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Stability Analysis of Distributed Order Fractional Chen System by H. Aminikhah, A. Refahi Sheikhani, H. Rezazadeh

“…We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. …”
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