Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

scholarly journals Construction of Solitary Two-Wave Solutions for a New Two-Mode Version of the Zakharov-Kuznetsov Equation

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1127 ◽  
Author(s):  
Imad Jaradat ◽  
Marwan Alquran
Keyword(s):  
Phase Velocity ◽  
Exact Solutions ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
Velocity Parameter ◽  
Interaction Dynamics ◽  
Wave Solutions ◽  
Proposed Model ◽  
Singular Soliton

A new two-mode version of the generalized Zakharov-Kuznetsov equation is derived using Korsunsky’s method. This dynamical model describes the propagation of two-wave solitons moving simultaneously in the same direction with mutual interaction that depends on an embedded phase-velocity parameter. Three different methods are used to obtain exact bell-shaped soliton solutions and singular soliton solutions to the proposed model. Two-dimensional and three-dimensional plots are also provided to illustrate the interaction dynamics of the obtained two-wave exact solutions upon increasing the phase-velocity parameter.

Dispersive soliton solutions for the Salerno equation for the nonlinear discrete electrical lattice in the forbidden bandgaps

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional ◽  
Bright Solitons ◽  
Jacobi Elliptic Function Method

In this paper, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear discrete electrical lattice in the forbidden bandgaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, three-dimensional and two-dimensional graphs are presented.

Establishment of High Precision Horizontal and Vertical Control Network in Zoucheng City

2013 ◽  
Vol 864-867 ◽  
pp. 2787-2791
Author(s):  
De Bao Wang ◽  
Yong Xiang Liu ◽  
Wen Jing Yang
Keyword(s):  
Fourth Order ◽  
Function Method ◽  
Three Dimensional ◽  
Geodetic Network ◽  
Control Network ◽  
Control Points ◽  
Two Dimensional ◽  
Level Control ◽  
Vertical Control ◽  
Free Network

The paper uses D level, E level and the level of GPS control network establishment satellite space geodetic network in Zoucheng city, through the baseline calculating, classic adjustment of free network, three-dimensional unconstrained adjustment and two-dimensional constraint adjustment to get the WGS-84 three dimensional coordinates and 1980 xi 'an horizontal coordinates of control points; then using the fourth-order levelling connection survey all D-level and part E-level control points to build vertical control network, for the remaining GPS control points we utilize quadric function method using GPS elevation fitting given its elevation seek to obtain three-dimensional coordinates of all the basic control points.

scholarly journals A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 309-316
Author(s):  
Gülnur Yel ◽  
Tolga Aktürk
Keyword(s):  
Exponential Function ◽  
Function Method ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Periodic Functions ◽  
New Approach ◽  
Wave Solutions ◽  
Exponential Function Method

AbstractIn this article, some new travelling wave solutions of the (3+1) dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation are obtained using the modified exponential function method. When the solution functions obtained are examined, it is seen that functions with periodic functions are obtained. Two and three dimensional graphs of the travelling wave solutions of the BLMP equation are drawn by selecting the appropriate parameters

Generalized exponential rational function method for extended Zakharov–Kuzetsov equation with conformable derivative

2019 ◽  
Vol 34 (20) ◽  
pp. 1950155 ◽  
Author(s):  
Behzad Ghanbari ◽  
M. S. Osman ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Function Method ◽  
Three Dimensional ◽  
Conformable Derivative ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Contour Plots ◽  
Free Parameters ◽  
Exponential Rational Function Method

In this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov–Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters.

The Establishment of D, E Grade GPS Control Network and Fourth-Order Leveling Network in Laicheng Industrial Zone of Laiwu City

2013 ◽  
Vol 846-847 ◽  
pp. 888-892
Author(s):  
De Bao Wang ◽  
Mei Lan Yu ◽  
Wen Jing Yang ◽  
Jun Feng Qu
Keyword(s):  
Fourth Order ◽  
Function Method ◽  
Three Dimensional ◽  
Geodetic Network ◽  
Control Network ◽  
Control Points ◽  
Two Dimensional ◽  
Industrial Zone ◽  
Level Control ◽  
Vertical Control

The paper uses D level,E level and the level of GPS control network establishment satellite space geodetic network in Laicheng industrial zone in Laiwu, through the baseline calculating, three-dimensional unconstrained adjustment and two-dimensional constraint adjustment to get the WGS-84 three dimensional coordinates and 1980 xi 'an horizontal coordinatesthe of control points; then using the fourth-order levelling connection survey all D-level, E-level control points and part GPS control points to build vertical control network, for the GPS control points of the remaining we utilize quadric function method using GPS elevation fitting given its elevation seek to obtain three-dimensional coordinates of all the basic control points.

scholarly journals Three-Dimensional Enclosures

2020 ◽  
pp. 621-672
Author(s):  
Steven L. Garrett
Keyword(s):  
Separation Of Variables ◽  
Three Dimensional ◽  
Normal Modes ◽  
Sound Field ◽  
Statistical Energy Analysis ◽  
Link Type ◽  
Wave Solutions ◽  
Different Shapes ◽  
The Individual ◽  
Degenerate Modes

Abstract In this chapter, solutions to the wave equation that satisfies the boundary conditions within three-dimensional enclosures of different shapes are derived. This treatment is very similar to the two-dimensional solutions for waves on a membrane of Chap. 10.1007/978-3-030-44787-8_6. Many of the concepts introduced in Sect. 10.1007/978-3-030-44787-8_6#Sec1 for rectangular membranes and Sect. 10.1007/978-3-030-44787-8_6#Sec5 for circular membranes are repeated here with only slight modifications. These concepts include separation of variables, normal modes, modal degeneracy, and density of modes, as well as adiabatic invariance and the splitting of degenerate modes by perturbations. Throughout this chapter, familiarity with the results of Chap. 10.1007/978-3-030-44787-8_6 will be assumed. The similarities between the standing-wave solutions within enclosures of different shapes are stressed. At high enough frequencies, where the individual modes overlap, statistical energy analysis will be introduced to describe the diffuse (reverberant) sound field.

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