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Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
Published 2013-01-01“…The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. …”
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22
Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media
Published 2013-01-01“…An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.…”
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23
On the Korteweg-de Vries equation: an associated equation
Published 1984-01-01“…The purpose of this paper is to describe a relationship between the Korteweg-de Vries (KdV) equation ut−6uux+uxxx=0and another nonlinear partial differential equation of the form zt+zxxx−3zxzxxz=H(t)z.The second equation will be called the Associated Equation (AE) and the connection between the two will be explained. …”
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24
On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method
Published 2021-01-01“…We have demonstrated that He’s approach is highly effective and powerful for the solution of such a higher-order nonlinear partial differential equation through our calculations and simulations. …”
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25
Shaping Single Offset Reflector Antennas Using Local Axis-Displaced Confocal Quadrics
Published 2016-01-01“…This work investigates a novel numerical procedure for the solution of an exact formulation for the Geometrical Optics synthesis of a single reflector antenna by simultaneously imposing Snell’s Law and Conservation of Energy in a tube of rays, yielding a second-order nonlinear partial differential equation of Monge-Ampère type, which can be solved as a boundary value problem. …”
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26
Steady Three-Dimensional MHD Mixed Convection Couple Stress Flow of Hybrid Nanofluid with Hall and Ion Slip Effect
Published 2022-01-01“…To transform the nonlinear partial differential equation to a nonlinear ordinary differential equation we used the defined similarity transformation. …”
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27
Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition
Published 2023-01-01“…To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. …”
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28
The significance of heat transfer through natural convection in stagnation point flow of prandtl fluid
Published 2025-01-01“…The analysis integrates velocity, concentration slips, and temperature jumps within a nonlinear partial differential equation framework. These equations are converted into nonlinear partial differential equations using appropriate dimensionless variables. …”
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29
A novel approach to construct optical solitons solutions of complex Ginzburg–Landau equation with five distinct forms of nonlinearities
Published 2025-02-01“…This paper presents a recently introduced innovative approach for analyzing closed-form solutions of nonlinear partial differential equations. While various methods exist for deriving closed-form solutions to many nonlinear evolution equations, additional solutions are still needed to study the various dynamics of physical systems governed by nonlinear partial differential equations. …”
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30
Higher Order Compact Finite Difference Schemes for Unsteady Boundary Layer Flow Problems
Published 2013-01-01“…This work extends its applications to nonlinear partial differential equations modelling unsteady boundary layer flows. …”
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31
Surfaces of a Constant Negative Curvature
Published 2012-01-01“…I study the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the nonlinear partial differential equations with constant Gaussian curvature .…”
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32
Classification of Exact Solutions for Generalized Form of Equation
Published 2013-01-01“…From here, we find some interesting results for nonlinear partial differential equations with generalized evolution.…”
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33
Global Well-Posedness and Determining Nodes of Non-Autonomous Navier–Stokes Equations with Infinite Delay on Bounded Domains
Published 2025-01-01“…The asymptotic behavior of solutions to nonlinear partial differential equations is an important tool for studying their long-term behavior. …”
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34
Benjamin-Ono Equation on a Half-Line
Published 2010-01-01“…We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.…”
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35
Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method
Published 2008-01-01“…The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.…”
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36
A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method
Published 2016-01-01“…This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. …”
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37
A Family of Novel Exact Solutions to 2+1-Dimensional KdV Equation
Published 2014-01-01“…We introduce two subequations with different independent variables for constructing exact solutions to nonlinear partial differential equations. In order to illustrate the efficiency and usefulness, we apply this method to 2+1-dimensional KdV equation, which was first derived by Boiti et al. (1986) using the idea of the weak Lax pair. …”
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38
Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation
Published 2021-01-01“…It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. …”
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39
Application of the Natural Decomposition Method to Strongly Coupled Partial Differential Equations: The Gray-Scott Model.
Published 2024“…By decomposing the nonlinear partial differential equations into a series of simpler equations, the method facilitates both analytical and numerical solutions, allowing for a detailed examination of the spatiotemporal patterns that emerge. …”
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40
Gluing for the Einstein constraint equations
Published 2025-01-01“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. …”
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