scholarly journals Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense

2021 ◽  
pp. 146134842110281
Author(s):  
Wael W. Mohammed ◽  
Hijaz Ahmad ◽  
Hamid Boulares ◽  
Fathi Khelifi ◽  
Mahmoud El-Morshedy
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Inverse Method ◽  
Multiplicative Noise ◽  
Major Benefit ◽  
Ode Method ◽  
3D Surfaces

In this article, the stochastic Hirota–Maccari system forced in the Itô sense by multiplicative noise is considered. We just use the He’s semi-inverse method, sine–cosine method, and Riccati–Bernoulli sub-ODE method to get new stochastic solutions which are hyperbolic, trigonometric, and rational. The major benefit of these three approaches is that they can be used to solve similar models. Furthermore, we plot 3D surfaces of analytical solutions obtained in this article by using MATLAB to illustrate the effect of multiplicative noise on the exact solution of the Hirota–Maccari method.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

THE TYPES OF AXISYMMETRIC EXACT SOLUTIONS CLOSELY RELATED TO n-SOLITONS FOR YANG–MILLS–HIGGS THEORY

1999 ◽  
Vol 14 (08n09) ◽  
pp. 585-592
Author(s):  
ZAI ZHE ZHONG
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Inverse Scattering ◽  
Real Matrix ◽  
Zakharov Equation ◽  
Yang Mills ◽  
Scattering Technique

In this letter, we point out that if a symmetric 2×2 real matrix M(ρ,z) obeys the Belinsky–Zakharov equation and | det (M)|=1, then an axisymmetric Bogomol'nyi field exact solution for the Yang–Mills–Higgs theory can be given. By using the inverse scattering technique, some special Bogomol'nyi field exact solutions, which are closely related to the true solitons, are generated. In particular, the Schwarzschild-like solution is a two-soliton-like solution.

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

scholarly journals Exact solution of fractional Nizhnik-Novikov-Veselov equation

2014 ◽  
Vol 18 (5) ◽  
pp. 1716-1717 ◽  
Author(s):  
Sui-Min Jia ◽  
Ming-Sheng Hu ◽  
Qiao-Ling Chen ◽  
Zhi-Juan Jia
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Function Method

The fractional Nizhnik-Novikov-Veselov equation is converted to its differential partner, and its exact solutions are successfully established by the exp-function method.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

scholarly journals General Method of Exact Solution of the Concentration?Dependent Diffusion Equation

1960 ◽  
Vol 13 (1) ◽  
pp. 1 ◽  
Author(s):  
JR Philip
Keyword(s):  
Exact Solution ◽  
Diffusion Equation ◽  
Exact Solutions ◽  
General Method

Only three forms of D(6) have previously been known to yield exact solutions of the equation

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

2021 ◽  
pp. 2150263
Author(s):  
A. Tripathy ◽  
S. Sahoo ◽  
S. Saha Ray ◽  
M. A. Abdou
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Ode Method ◽  
Novel Methods

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

Sign in / Sign up

Export Citation Format

Share Document