Exploration of the soliton solutions of the (n+1) dimensional generalized Kadomstev Petviashvili equation using an innovative approach by Bahadır Kopçasız, Fatma Nur Kaya Sağlam, Hasan Bulut, Taha Radwan

“…Its integrability and rich soliton dynamics continue to attract researchers interested in the field of nonlinear partial differential equations (NLPDEs). …”
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A New Efficient Hybrid Method Based on FEM and FDM for Solving Burgers’ Equation with Forcing Term by Aysenur Busra Cakay, Selmahan Selim

“…The resulting system of the nonlinear ordinary differential equations is then solved using MATLAB computer codes at each time step. …”
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Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with p-Laplacian Operator by Min Jiang, Shouming Zhong

“…By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations with p-Laplacian operator in terms of different value of parameter. …”
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Acoustic streaming induced by the non-periodic sound in a viscous medium by Anna Perelomova

“…This last term equals exactly zero for periodic sound (after averaging) and differs from zero for other types of sound. Sound itself must satisfy the well-known Khokhlov–Zabolotskaya–Kuznetsov equation describing the weakly diffracting nonlinear acoustic beam propagating over viscous thermconducting fluid. …”
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Modeling and Exploration of Localized Wave Phenomena in Optical Fibers Using the Generalized Kundu–Eckhaus Equation for Femtosecond Pulse Transmission by Ejaz Hussain, Ali H. Tedjani, Khizar Farooq, Beenish

“…This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. …”
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Analytical Approximate Solutions of Caputo Fractional KdV-Burgers Equations Using Laplace Residual Power Series Technique by Aliaa Burqan, Mona Khandaqji, Zeyad Al-Zhour, Ahmad El-Ajou, Tasneem Alrahamneh

“…The KdV-Burgers equation is one of the most important partial differential equations, established by Korteweg and de Vries to describe the behavior of nonlinear waves and many physical phenomena. …”
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Nonlinear forced response of non-uniform beams carrying point masses using the harmonic balance method with an arc-length continuation scheme by Ma’en S Sari

“…By the means of Newton’s second law of motion, the integro-partial differential equation of motion is derived. …”
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Hamiltonian conserved Crank-Nicolson schemes for a semi-linear wave equation based on the exponential scalar auxiliary variables approach by Huanhuan Li, Lei Kang, Meng Li, Xianbing Luo, Shuwen Xiang

“…The keys to constructing numerical schemes for nonlinear partial differential equations are accuracy, handling of the nonlinear terms, and physical properties (energy dissipation or conservation). …”
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Climate sensitivity and attribution analysis of water resources in China by Youzhu Zhao, Qiuxiang Jiang, Zilong Wang

“…Based on sensitivity analysis, TWS responses are categorized into distinct sensitivity categories. Through a partial least squares structural equation model, the study identifies a significant positive effect of climate changes on TWS across all sensitivity categories, while human activities tend to have a negative impact. …”
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Impacts of sinusoidal heat flux and embraced heated rectangular cavity on natural convection within a square enclosure partially filled with porous medium and Casson-hybrid nanoflu... by Ahlawat Anil, Sharma Mukesh Kumar, Ghachem Kaouther, Alshammari Badr M., Kolsi Lioua

“…The sinusoidal heat flux of length H/2 is positioned centrally at the enclosure’s bottom wall, although the top wall is at a lower temperature, say T c, and the rest of the enclosure was insulated. The finite-difference method, combined with the successive over relaxation, successive under relaxation, and Gauss–Siedel techniques, is employed to address the challenge of solving the nonlinear coupled governing partial differential equations of motion and energy. …”
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The data-driven localized wave solutions of KdV-type equations via physics-informed neural networks with a priori information by Zhi-Ying Feng, Xiang-Hua Meng, Xiao-Ge Xu

“…By comparing the results of pr-PINNs with PINNs under the same configuration, pr-PINNs show higher accuracy and lower cost in solving different solutions of nonlinear evolution equations due to the combination of the priori information with PINNs, which enables the neural network to capture the characteristics of the solution during training. …”
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A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion by O. H. Galal

“…Galerkin projection is used in converting the original stochastic partial differential equation (PDE) into a set of coupled deterministic partial differential equations and then solved using finite difference method. …”
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Numerical solution of a PDE arising from prediction with expert advice by Jeff Calder, Nadejda Drenska, Drisana Mosaphir

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An analysis of upper-convected Maxwell nanofluid flow over a stretching surface: Theoretical and numerical approaches by Baskaran Yamuna, Athimoolam Meena, Lakshmanan Rajendran, Mohammad Izadi

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Numerous Multi-Wave Solutions of the Time-Fractional Boussinesq-like System via a Variant of the Extended Simple Equations Method (SEsM) by Elena V. Nikolova, Mila Chilikova-Lubomirova

“…In this study, we propose a generalized framework based on the Simple Equations Method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). …”
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Traveling wave solutions of a hybrid KdV-Burgers equation with arbitrary real coefficients in relation with beam-permeated multi-ion plasma fluids by Kuldeep Singh, Steffy Sara Varghese, Ioannis Kourakis

“…Abstract The Korteweg de Vries-Burgers (KdV-B) (1+1) equation $$\begin{aligned} \frac{\partial \psi }{\partial t} +a \, \psi \frac{\partial \psi }{\partial x} + b \, \frac{\partial ^{3}\psi }{\partial x^{3}} = c \, \frac{\partial ^{2} \psi }{\partial x^2} \,, \end{aligned}$$ incorporating constant (real) coefficients representing nonlinearity (a), dispersion (b) and dissipation (c), is a long known paradigm in e.g. plasma physics, where it can be derived from plasma fluid-dynamical models, so that all coefficients depend parametrically on the plasma composition. …”
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Non-local operator as a mathematical tool to improve the modeling of water pollution phenomena in environmental science: A spatio-temporal approach by Pasquini Fotsing Soh, Mathew Kinyanjui, David Malonza, Roy Kiogora

“…Firstly, we formulate and analyze a nonlinear ordinary differential equations model that integrates a fractional derivative to capture the memory effect of pollutants in water. …”
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Coupled of Semi Analytic Approach Associated with Laplace Transform First Step for Solving Matrix Differential Equations Quadratic Form when the Time-Delay in Noise Term by Khalid Hammood AL-Jizani

“…This technique can used to different nonlinear problem. The Adomian decomposition method is a semi analytical technique for solving different type of differential equations ordinary, partial, fractional, delay differential equations and many type. …”
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Different Approximations to the Solution of Upper-Convected Maxwell Fluid over a Porous Stretching Plate by Vasile Marinca, Remus-Daniel Ene, Bogdan Marinca, Romeo Negrea

“…In the present paper, we consider an incompressible magnetohydrodynamic flow of two-dimensional upper-convected Maxwell fluid over a porous stretching plate with suction and injection. The nonlinear partial differential equations are reduced to an ordinary differential equation by the similarity transformations and taking into account the boundary layer approximations. …”
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A toxin-mediated size-structured population model: Finite difference approximation and well-posedness by Qihua Huang, Hao Wang

“…Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). …”
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