Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth by Ping Wang, Zunshui Cheng

“…The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. …”
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New super and shock like solitary structures for KdV equation with higher-order nonlinearity by H.S. Alayachi, Abdulghani Alharbi, E.K. El-Shewy, Mahmoud A.E. Abdelrahman

“…The modified F-expansion approach is an effective, powerful and straightforward method for obtaining the solitary wave solutions to the nonlinear partial differential equations (NPDEs). The effect of model parameters on the nature, properties and structures of the model solutions have been examined. …”
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MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical... by J. Bouslimi, M. Omri, R. A. Mohamed, K. H. Mahmoud, S. M. Abo-Dahab, M. S. Soliman

“…The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. …”
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Optical soliton solutions of the M-fractional paraxial wave equation by Md. Habibul Bashar, Md. Abde Mannaf, M. M. Rahman, Mst. Tania Khatun

“…The strategy introduced is fundamental and robust as a smart soliton solution for nonlinear partial differential equations, and it may play a crucial role in nonlinear optics, fiber optics, and communication systems.…”
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Lie-symmetry analysis of a three dimensional flow due to unsteady stretching of a flat surface with non-uniform temperature distribution by Ghani Khan, Muhammad Safdar, Safia Taj, Adnan Munir, Muhammad Tauseef Nasir

“…Twelve Lie point symmetries for the nonlinear partial differential equations describing the considered flow and heat transfer phenomena are derived. …”
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Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions by Akhtar Hussain, Tarek F. Ibrahim, F. M. Osman Birkea, Abeer M. Alotaibi, Bushra R. Al-Sinan, Herbert Mukalazi

“…Abstract Despite the historical position of the F-expansion method as a method for acquiring exact solutions to nonlinear partial differential equations (PDEs), this study highlights its superiority over alternative auxiliary equation methods. …”
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Computational Study on Three-Dimensional Convective Casson Nanofluid Flow past a Stretching Sheet with Arrhenius Activation Energy and Exponential Heat Source Effects by P. Ragupathi, S. Saranya, H.V.R. Mittal, Qasem M. Al-Mdallal

“…The developed model of nonlinear partial differential equations (PDEs) has been transformed into ordinary differential equations (ODEs) using similarity transformations. …”
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Analysis of Model Parameters for a Polymer Filtration Simulator by N. Brackett-Rozinsky, S. Mondal, K. R. Fowler, E. W. Jenkins

“…The simulator is a three-dimensional, time-dependent discretization of a coupled system of nonlinear partial differential equations used to model fluid flow and debris transport, along with statistical relationships that define debris distributions and retention probabilities. …”
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Effects of Thermodiffusion and Chemical Reaction on Magnetohydrodynamic-Radiated Unsteady Flow Past an Exponentially Accelerated Inclined Permeable Plate Embedded in a Porous Mediu... by B. Prabhakar Reddy, M. H. Simba, Alfred Hugo

“…The governing nondimensional set of coupled nonlinear partial differential equations with related initial and boundary conditions are solved numerically by using the accurate and efficient DuFort–Frankel’s explicit finite difference method. …”
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The Effects of Activation Energy and Thermophoretic Diffusion of Nanoparticles on Steady Micropolar Fluid along with Brownian Motion by Zulqurnain Sabir, Assad Ayub, Juan L. G. Guirao, Saira Bhatti, Syed Zahir Hussain Shah

“…The nonlinear partial differential equations are converted into nonlinear ordinary differential equations, and a famous shooting scheme is used to present the numerical solutions. …”
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Solutions of Cauchy Problems for the Caudrey–Dodd–Gibbon–Kotera–Sawada Equation in Three Spatial and Two Temporal Dimensions by Yufeng Zhang, Linlin Gui

“…Fokas has obtained integrable nonlinear partial differential equations (PDEs) in 4 + 2 dimensions by complexifying the independent variables. …”
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Combined Effects of Thermal Radiation and Nanoparticles on Free Convection Flow and Heat Transfer of Casson Fluid over a Vertical Plate by M. G. Sobamowo

“…The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equations through similarity transformations. …”
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On nonlinear coupled differential system for heat transfer in magnetized enclosure with T-shaped baffle by using machine learning by Khalil Ur Rehman, Wasfi Shatanawi, Lok Yian Yian

“…It is well consensus among researchers that the constructing mathematical model for heat transfer problems results set of coupled nonlinear partial differential equations (PDEs) and the solution in this regard gets a challenging task. …”
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Fast Attitude Maneuver of a Flexible Spacecraft with Passive Vibration Control Using Shunted Piezoelectric Transducers by Bassam A. Albassam

“…The control design process starts with deriving the nonlinear partial differential equations of motion for the spacecraft using Hamilton’s principle which accounts for the electromechanical coupling and the presence of resistive or resistive-inductive circuits. …”
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Thermo-Magneto-Solutal Squeezing Flow of Nanofluid between Two Parallel Disks Embedded in a Porous Medium: Effects of Nanoparticle Geometry, Slip and Temperature Jump Conditions by M. G. Sobamowo, A. T. Akinshilo, A. A. Yinusa

“…Similarity variables are used to transform the developed governing systems of nonlinear partial differential equations to systems of nonlinear ordinary differential equations. …”
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New exact soliton wave solutions appear in optical fibers with Sardar sub equation and new auxiliary equation techniques by Umair Asghar, Muhammad Imran Asjad, Yasser Salah Hamed, Ali Akgul, Murad Khan Hassani

“…These methods are applied to derive a wide range of soliton solutions for nonlinear partial differential equations. By transforming the original partial differential equation into an ordinary differential equation using an appropriate transformation, various types of solitary wave solutions are obtained. …”
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Machine learning-driven analysis of heat transfer in chemically reactive fluid flow considering Soret-Dufour effects by Shazia Habib, Saleem Nasir, Zeeshan Khan, Abdallah S. Berrouk, Waseem, Saeed Islam

“…By transforming the governing system of nonlinear partial differential equations into ordinary differential equations via similarity transformation, the methodology attains computational efficiency and solution precision. …”
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Applications of the neuro-evolutionary approach to the parabolic type partial differential equations by Waseem, Asad Ullah, Emad A.A. Ismail, Fuad A. Awwad

“…This work aims to investigate the Cuckoo search-active set algorithm (CS-ASA), which is based on the artificial neural network (ANN) approach to the nonlinear partial differential equations (PDEs). CS-ASA technique modifies the Cuckoo search best possible solution to the next stage. …”
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Numerical analysis of mathematical model of nanofluid flow through stagnation point involving thermal radiation, activation energy, and living organisms by Munaza Chaudhry, Muhammad Abdul Basit, Muhammad Imran, Madeeha Tahir, Aiedh Mrisi Alharthi, Jihad Younis

“…To explain the flow model’s physical significance, zero mass flux condition has been employed at the surface. Nonlinear partial differential equations are transformed into a collection of linked ordinary differential equations via similarity transformations. …”
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Mathematical Modeling of Wax Deposition in Field-Scale Crude Oil Pipeline Systems by Francis Oketch Ochieng, Mathew Ngugi Kinyanjui, Jeconia Okelo Abonyo, Phineas Roy Kiogora

“…The coupled nonlinear partial differential equations governing the flow are discretized in time by a second-order semi-implicit time discretization scheme based on the Adams-Bashforth and Crank-Nicolson methods, which completely decouples the computation of the governing equations. …”
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