scholarly journals Modified Kudrayshov Method to Solve Generalized Kuramoto–Sivashinsky Equation

2018 ◽  
Author(s):  
Adem Kilicman ◽  
Rathinavel Silambarasan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Exact Solutions ◽  
Exact Analytical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Complex Structures ◽  
Algebraic Equations ◽  
Uniqueness Of Solutions ◽  
Sivashinsky Equation

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

scholarly journals Modified Kudrayshov Method to Solve Generalized Kuramoto–Sivashinsky Equation

2018 ◽  
Author(s):  
Rathinavel Silambarasan ◽  
Adem Kilicman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Complex Plane ◽  
Exact Analytical Solution ◽  
Nonlinear Partial Differential Equation ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Complex Solutions ◽  
Sivashinsky Equation

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov equation for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations by results of various steps which on solving the so obtained equation systems yields the analytical solution. By this way various exact including complex solutions are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of various solutions.

scholarly journals Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 527 ◽  
Author(s):  
Adem Kilicman ◽  
Rathinavel Silambarasan
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Complex Structures ◽  
Algebraic Equations ◽  
New Exact Solutions ◽  
Modified Kudryashov Method ◽  
Kudryashov Method ◽  
The Given ◽  
Sivashinsky Equation

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems yields the analytical solution. By this way, various exact solutions including complex structures are found, and their behavior is drawn in the 2D plane by Maple to compare the uniqueness and wave traveling of the solutions.

scholarly journals On a nonlinear PDE involving weighted $p$-Laplacian

2019 ◽  
Vol 38 (5) ◽  
pp. 131-145
Author(s):  
A. El Khalil ◽  
M. D. Morchid Alaoui ◽  
Mohamed Laghzal ◽  
A. Touzani
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Method ◽  
Nonlinear Partial Differential Equation ◽  
Weighted Sobolev Spaces ◽  
Point Theory ◽  
Energy Functional ◽  
Nonlinear Pde ◽  
Laplacian Operator ◽  
Uniqueness Of Solutions

In the present paper, we study the nonlinear partial differential equation with the weighted $p$-Laplacian operator\begin{gather*}- \operatorname{div}(w(x)|\nabla u|^{p-2}\nabla u) = \frac{ f(x)}{(1-u)^{2}},\end{gather*}on a ball ${B}_{r}\subset \mathbb{R}^{N}(N\geq 2)$. Under some appropriate conditionson the functions $f, w$ and the nonlinearity $\frac{1}{(1-u)^{2}}$, we prove the existence and the uniqueness of solutions of the above problem. Our analysis mainly combines the variational method and critical point theory. Such solution is obtained as a minimizer for the energy functional associated with our problem in the setting of the weighted Sobolev spaces.

scholarly journals Transient-False Method for Solving System of Nonlinear Partial Differential Equations

2018 ◽  
Vol 1 (25) ◽  
pp. 509-522
Author(s):  
. Ali Khalaf Hussain
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Linear Algebraic Equations

          In this paper we study the false transient method  to  solve and transform a system of non-linear partial differential equations which can be solved using finite-difference method and give some problems which have a good results compared with the exact solution, whereas this method was used to transform the nonlinear partial differential equation to a linear partial differential equation which can be solved by using the alternating-direction implicit method after using the ADI method. The system of linear algebraic equations could be obtained and can be solved by using MATLAB.

EXACT SOLUTIONS FOR INTERFACIAL OUTFLOWS WITH STRAINING

2014 ◽  
Vol 55 (3) ◽  
pp. 232-244 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
MICHAEL A. BRIDESON
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Point Source ◽  
Exact Solutions ◽  
Closed Form ◽  
Line Source ◽  
Nonlinear Partial Differential Equation ◽  
Background Flow ◽  
Closed Form Solutions ◽  
Fluid Instabilities

AbstractIn models of fluid outflows from point or line sources, an interface is present, and it is forced outwards as time progresses. Although various types of fluid instabilities are possible at the interface, it is nevertheless of interest to know the development of its overall shape with time. If the fluids on either side are of nearly equal densities, it is possible to derive a single nonlinear partial differential equation that describes the interfacial shape with time. Although nonlinear, this equation admits a simple transformation that renders it linear, so that closed-form solutions are possible. Two such solutions are illustrated; for a line source in a planar straining flow and a point source in an axisymmetric background flow. Possible applications in astrophysics are discussed.

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