scholarly journals Direct method for solving nonlinear strain wave equation in microstructure solids

2016 ◽  
Vol 11 (10) ◽  
pp. 121-131 ◽  
Author(s):  
A Gepreel Khaled ◽  
A Nofal Taher ◽  
S Al Sayali Nehal
Keyword(s):  
Wave Equation ◽  
Direct Method ◽  
Strain Wave ◽  
Nonlinear Strain

Abundant exact solutions to the strain wave equation in micro-structured solids

2021 ◽  
pp. 2150439
Author(s):  
Karmina K. Ali ◽  
R. Yilmazer ◽  
H. Bulut ◽  
Tolga Aktürk ◽  
M. S. Osman
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Exact Solutions ◽  
Rational Function ◽  
Physical Interpretation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Singular Solutions ◽  
Strain Wave ◽  
Important Place

In this study, the strain wave equation in micro-structured solids which take an important place in solid physics is presented for consideration. The generalized exponential rational function method is used for this purpose which is one of the most powerful methods of constructing abundantly distinct, exact solutions of nonlinear partial differential equations. In micro-structured solids, wave propagation is based on the structure of the strain wave equation. As a consequence, we successfully received many different exact solutions, including non-topological solutions, periodic singular solutions, topological solutions, singular solutions, like periodic lump solutions. Furthermore, in order to better understand their physical interpretation, 2D, 3D, and counter plots are graphed for each of the solutions acquired.

scholarly journals Diversity of Interaction Solutions of a Shallow Water Wave Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Jian-Ping Yu ◽  
Wen-Xiu Ma ◽  
Bo Ren ◽  
Yong-Li Sun ◽  
Chaudry Masood Khalique
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
General Theory ◽  
Shallow Water ◽  
Water Wave ◽  
Direct Method ◽  
Soliton Solutions ◽  
Interaction Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions

In this paper, we study the diversity of interaction solutions of a shallow water wave equation, the generalized Hirota–Satsuma–Ito (gHSI) equation. Using the Hirota direct method, we establish a general theory for the diversity of interaction solutions, which can be applied to generate many important solutions, such as lumps and lump-soliton solutions. This is an interesting feature of this research. In addition, we prove this new model is integrable in Painlevé sense. Finally, the diversity of interactive wave solutions of the gHSI is graphically displayed by selecting specific parameters. All the obtained results can be applied to the research of fluid dynamics.

Fourth order wave equation with nonlinear strain and logarithmic nonlinearity

2019 ◽  
Vol 141 ◽  
pp. 185-205 ◽  
Author(s):  
Runzhang Xu ◽  
Wei Lian ◽  
Xiangkun Kong ◽  
Yanbing Yang
Keyword(s):  
Wave Equation ◽  
Fourth Order ◽  
Nonlinear Strain ◽  
Fourth Order Wave Equation

Application of Kudryashov and functional variable methods to the strain wave equation in microstructured solids

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Z. Ayati ◽  
K. Hosseini ◽  
M. Mirzazadeh
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Exact Solutions ◽  
Symbolic Computation ◽  
Strain Wave ◽  
Functional Variable

AbstractThe aim of this paper is to obtain the exact solutions of the strain wave equation applied for illustrating wave propagation in microstructured solids. The effective Kudryashov and functional variable methods along with the symbolic computation system have been used to accomplish the purpose.

scholarly journals Algebraic Method of Solution of Schrödinger’s Equation ofa Quantum Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Quantum Dot ◽  
Direct Method ◽  
Algebraic Method ◽  
Time Dependent ◽  
Quantum Model ◽  
Decomposition Technique ◽  
Method Of Solution ◽  
Schrödinger's Equation

This work is aiming to show the advantage of using the Lie algebraic decomposition technique to solvefor Schrödinger’s wave equation for a quantum model, compared with the direct method of solution. The advantageis a two-fold: one is to derive general form of solution, and, two is relatively manageable to deal with the case oftime-dependent system Hamiltonian. Specifically, we consider the model of 2-level optical atom and solve for thecorresponding Schrödinger’s wave equation using the Lie algebraic decomposition technique. The obtained formof solution for the wave function is used to examine computationally the atomic localization in the coordinate space.For comparison, the direct method of solution of the wave function is analysed in order to show its complicationwhen dealing with time-dependent Hamiltonian.The possibility of using the Lie algebraic method for a qubit model(a driven quantum dot model) is briery discussed, if Schrödinger’s wave function is to be examined for the qubitlocalization.

scholarly journals Nonlinear strain wave localization in periodic composites

2012 ◽  
Vol 49 (23-24) ◽  
pp. 3381-3387 ◽  
Author(s):  
A.V. Porubov ◽  
I.V. Andrianov ◽  
V.V. Danishevs’kyy
Keyword(s):  
Wave Localization ◽  
Strain Wave ◽  
Nonlinear Strain ◽  
Periodic Composites

scholarly journals Copious Closed Forms of Solutions for the Fractional Nonlinear Longitudinal Strain Wave Equation in Microstructured Solids

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Haiyong Qin ◽  
Mostafa M. A. Khater ◽  
Raghda A. M. Attia
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Longitudinal Strain ◽  
Rational Functions ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Strain Wave ◽  
Integer Order ◽  
Wave Solutions

A computational scheme is employed to investigate various types of the solution of the fractional nonlinear longitudinal strain wave equation. The novelty and advantage of the proposed method are illustrated by applying this model. A new fractional definition is used to convert the fractional formula of these equations into integer-order ordinary differential equations. Soliton, rational functions, the trigonometric function, the hyperbolic function, and many other explicit wave solutions are obtained.

Novel exact double periodic Soliton solutions to strain wave equation in micro structured solids

2020 ◽  
Vol 550 ◽  
pp. 124077
Author(s):  
Amna Irshad ◽  
Naveed Ahmed ◽  
Aqsa Nazir ◽  
Umar Khan ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Strain Wave
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