scholarly journals Soliton solution of Generalized Zakharov-Kuznetsov and ZakharovKuznetsov-Benjamin-Bona-Mahoney equations with conformable temporal evolution

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Hadi Rezazadeh ◽  
Alper Korkmaz ◽  
Nauman Reza ◽  
Khalid Ali ◽  
Mostafa Eslami
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Soliton Solution ◽  
Temporal Evolution ◽  
Soliton Solutions ◽  
Trigonometric Functions ◽  
Partial Differential ◽  
Functional Variable

In this paper, we proposethe method of functional variable for finding soliton solutions of two practical problems arising in electronics, namely, the conformable time-conformable Generalized Zakharov-Kuznetsov equation (GZKE) and the conformable time-conformable Generalized Zakharov-Kuznetsov-Benjamin-BonaMahoney equation (GZK-BBM). The soliton solutions are expressed by two types of functions which are hyperbolic and trigonometric functions. Implemented method is more effective, powerful and straightforward to construct the soliton solutions for nonlinear conformable time-conformable partial differential equations.

scholarly journals On the influence of the initial data in a combustion problem

1980 ◽  
Vol 22 (2) ◽  
pp. 193-209 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Temporal Evolution ◽  
Initial Conditions ◽  
Coupled System ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Approximate Expressions ◽  
Combustion Problem

AbstractThe combustion of a material can be modelled by two coupled parabolic partial differential equations for the temperature and concentration of the material. This paper deals with properties of the solution of these equations inside a cylinder or a sphere and under given initial conditions. Bounds for the variation of the temperature with the initial conditions are first established by considering a decoupled form of the equations. Then the coupled system is used to obtain approximate expressions for the temporal evolution of temperature and concentration.

scholarly journals Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Paul Bracken
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Partial Differential ◽  
Intrinsic Geometry ◽  
Integrable Equations ◽  
Higher Dimensional ◽  
Riemannian Spaces

The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric for the space. The manifolds of interest are surfaces and higher-dimensional Riemannian spaces. Methods for specifying integrable evolutions of surfaces by means of these equations will also be presented.

scholarly journals The New Simulation of Quasiperiodic Wave, Periodic Wave, and Soliton Solutions of the KdV-mKdV Equation via a Deep Learning Method

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Yong Zhang ◽  
Huanhe Dong ◽  
Jiuyun Sun ◽  
Zhen Wang ◽  
Yong Fang ◽  
...  
Keyword(s):  
Deep Learning ◽  
Partial Differential Equations ◽  
Initial Data ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Mkdv Equation ◽  
Learning Method ◽  
Partial Differential

How to solve the numerical solution of nonlinear partial differential equations efficiently and conveniently has always been a difficult and meaningful problem. In this paper, the data-driven quasiperiodic wave, periodic wave, and soliton solutions of the KdV-mKdV equation are simulated by the multilayer physics-informed neural networks (PINNs) and compared with the exact solution obtained by the generalized Jacobi elliptic function method. Firstly, the different types of solitary wave solutions are used as initial data to train the PINNs. At the same time, the different PINNs are applied to learn the same initial data by selecting the different numbers of initial points sampled, residual collocation points sampled, network layers, and neurons per hidden layer, respectively. The result shows that the PINNs well reconstruct the dynamical behaviors of the quasiperiodic wave, periodic wave, and soliton solutions for the KdV-mKdV equation, which gives a good way to simulate the solutions of nonlinear partial differential equations via one deep learning method.

scholarly journals A Boiti-Leon Pimpinelli equations with time-conformable derivative

2019 ◽  
Vol 9 (3) ◽  
pp. 95-101 ◽  
Author(s):  
Kamal Ait Touchent ◽  
Zakia Hammouch ◽  
Toufik Mekkaoui ◽  
Canan Unlu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Gordon Equation ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Hyperbolic Functions ◽  
Partial Differential ◽  
Expansion Technique

In this paper, we derive some new soliton solutions to $(2+1)$-Boiti-Leon Pempinelli equations with conformable derivative by using an expansion technique based on the Sinh-Gordon equation. The obtained solutions have different expression such as trigonometric, complex and hyperbolic functions. This powerful and simple technique can be used to investigate solutions of other  nonlinear partial differential equations.

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