scholarly journals A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator

2022 ◽  
Vol 30 (1) ◽  
pp. 335-361
Author(s):  
Melih Cinar ◽  
◽  
Ismail Onder ◽  
Aydin Secer ◽  
Mustafa Bayram ◽  
...  
Keyword(s):  
Dynamical System ◽  
Differential Operator ◽  
Exact Solutions ◽  
3D Graphics ◽  
Langmuir Waves ◽  
New Exact Solutions ◽  
Different Types ◽  
Pde Systems ◽  
2D And 3D ◽  
Linear Pdes

<abstract><p>This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used to solve the considered system. The paper also includes a comparison between the solutions of the models containing separately conformable and $ M- $ truncated derivatives. The solutions are compared in the $ 2D $ and $ 3D $ graphics. All computations and representations of the solutions are fulfilled with the help of Mathematica 12. The methods are efficient and easily computable, so they can be applied to get exact solutions of non-linear PDEs (or PDE systems) with the different types of derivatives.</p></abstract>

New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method

2021 ◽  
pp. 2150163
Author(s):  
Seyed Mehdi Mirhosseini-Alizamini ◽  
Najib Ullah ◽  
Jamilu Sabi’u ◽  
Hadi Rezazadeh ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Physical Phenomenon ◽  
Ocean Engineering ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Different Types

In this work, we investigate a new Kudryashov method (NKM) to find the exact and some new solutions of four different types of nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). This is an appropriate algorithm for finding the exact solutions and also working for different types of nonlinear confirmable differential equations. In coastal and ocean engineering, some physical phenomenon is based on the exact solutions of the NLACBEs.

Rogue waves generation and interaction of multipeak rational solitons in the system of equations for the ion sound and Langmuir waves

2019 ◽  
Vol 33 (24) ◽  
pp. 1950277 ◽  
Author(s):  
Iftikhar Ahmed ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Rogue Wave ◽  
Soliton Solutions ◽  
Quadratic Function ◽  
Rogue Waves ◽  
System Of Equations ◽  
3D Graphics ◽  
Langmuir Waves ◽  
Double Exponential ◽  
Different Types ◽  
Multiwave Solutions

In this paper, our purpose is to construct multiwave solutions for the system of equations for the ion sound and Langmuir waves (SEISLWs) by utilizing the traveling wave and logarithmic transformation with the help of symbolic computation and the ansatz function method. We apply three distinctive approaches: namely, positive quadratic function approach, three waves approach and double exponential approach. By choosing suitable parametric values, 3D graphics are plotted to get different types of multiwave solutions including lump waves, rogue wave and multipeak soliton solutions. Moreover, we revealed very interesting multiwaves interactional phenomena.

New exact solutions for coupled nonlinear system of ion sound and Langmuir waves

2019 ◽  
Vol 94 (6) ◽  
pp. 885-894 ◽  
Author(s):  
M Shakeel ◽  
M A Iqbal ◽  
Q Din ◽  
Q M Hassan ◽  
K Ayub
Keyword(s):  
Nonlinear System ◽  
Exact Solutions ◽  
Langmuir Waves ◽  
New Exact Solutions

scholarly journals On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Coatings ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1429
Author(s):  
Muhammad Imran Asjad ◽  
Hamood Ur Rehman ◽  
Zunaira Ishfaq ◽  
Jan Awrejcewicz ◽  
Ali Akgül ◽  
...  
Keyword(s):  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
3D Graphics ◽  
New Exact Solutions ◽  
Hyperbolic Function Method ◽  
The Common ◽  
2D And 3D ◽  
Exact Soliton Solutions

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

scholarly journals The system of equations for the ion sound and Langmuir waves and its new exact solutions

2018 ◽  
Vol 9 ◽  
pp. 1631-1634 ◽  
Author(s):  
Aly R. Seadawy ◽  
D. Kumar ◽  
K. Hosseini ◽  
F. Samadani
Keyword(s):  
Exact Solutions ◽  
System Of Equations ◽  
Langmuir Waves ◽  
New Exact Solutions

New Exact Solutions of Steady Plane Flows of an In Compressible Fluid of Variable Viscosity

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Sobia Younus
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Compressible Fluid ◽  
Variable Viscosity ◽  
Plane Motion ◽  
Transformation Technique ◽  
Vorticity Distribution ◽  
New Exact Solutions ◽  
Steady Plane ◽  
Uniform Stream

<span>Some new exact solutions to the equations governing the steady plane motion of an in compressible<span> fluid of variable viscosity for the chosen form of the vorticity distribution are determined by using<span> transformation technique. In this case the vorticity distribution is proportional to the stream function<span> perturbed by the product of a uniform stream and an exponential stream<br /><br class="Apple-interchange-newline" /></span></span></span></span>

scholarly journals Deep Learning Methods for Classification of Certain Abnormalities in Echocardiography

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 495
Author(s):  
Imayanmosha Wahlang ◽  
Arnab Kumar Maji ◽  
Goutam Saha ◽  
Prasun Chakrabarti ◽  
Michal Jasinski ◽  
...  
Keyword(s):  
Deep Learning ◽  
Short Term Memory ◽  
Support Vector ◽  
Variational Autoencoder ◽  
Different Types ◽  
Static Images ◽  
Long Short Term Memory ◽  
2D And 3D ◽  
Better Than

This article experiments with deep learning methodologies in echocardiogram (echo), a promising and vigorously researched technique in the preponderance field. This paper involves two different kinds of classification in the echo. Firstly, classification into normal (absence of abnormalities) or abnormal (presence of abnormalities) has been done, using 2D echo images, 3D Doppler images, and videographic images. Secondly, based on different types of regurgitation, namely, Mitral Regurgitation (MR), Aortic Regurgitation (AR), Tricuspid Regurgitation (TR), and a combination of the three types of regurgitation are classified using videographic echo images. Two deep-learning methodologies are used for these purposes, a Recurrent Neural Network (RNN) based methodology (Long Short Term Memory (LSTM)) and an Autoencoder based methodology (Variational AutoEncoder (VAE)). The use of videographic images distinguished this work from the existing work using SVM (Support Vector Machine) and also application of deep-learning methodologies is the first of many in this particular field. It was found that deep-learning methodologies perform better than SVM methodology in normal or abnormal classification. Overall, VAE performs better in 2D and 3D Doppler images (static images) while LSTM performs better in the case of videographic images.

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