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.

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 New Soliton Solutions of The Nonlinear Radhakrishnan-Kundu-Lakshmanan Equation With the Beta-Derivative

2021 ◽  
Author(s):  
Yusuf Pandir ◽  
Yusuf Gurefe ◽  
Tolga Akturk
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Two Dimensional ◽  
New Exact Solutions ◽  
Definition Of ◽  
Exponential Function Method

Abstract In this article, the modified exponential function method is applied to find the exact solutions of the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative. The definition of the conformable beta derivative and its properties proposed by Atangana are given. With the proposed method, exact solutions of the nonlinear Radhakrishnan-Kundu-Lakshmanan equation which can be stated with the conformable beta-derivative of Atangana are obtained. The exact solutions found as a result of the application of the method seem to be 1-soliton solutions, dark soliton solutions, periodic soliton solutions and rational function solutions. According to the obtained results, we can say that the Radhakrishnan-Kundu-Lakshmanan equation with Atangana’s conformable beta-derivative have different soliton solutions. Also, three-dimensional contour and density graphs and two- dimensional graphs drawn with different parameters are given of these new exact solutions.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

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.

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.

Symbolic computation study on exact solutions to a generalized (3+1)-dimensional Kadomtsev-Petviashvili-type equation

2020 ◽  
pp. 2150116
Author(s):  
Cheng-Cheng Zhou ◽  
Xing Lü ◽  
Hai-Tao Xu
Keyword(s):  
Numerical Simulation ◽  
Exact Solutions ◽  
Prime Number ◽  
Symbolic Computation ◽  
Three Dimensional ◽  
Type Equation ◽  
Two Dimensional ◽  
Type Solution ◽  
Bilinear Operators ◽  
Number Formula

Based on the prime number [Formula: see text], a generalized (3+1)-dimensional Kadomtsev-Petviashvili (KP)-type equation is proposed, where the bilinear operators are redefined through introducing some prime number. Computerized symbolic computation provides a powerful tool to solve the generalized (3+1)-dimensional KP-type equation, and some exact solutions are obtained including lump-type solution and interaction solution. With numerical simulation, three-dimensional plots, density plots, and two-dimensional curves are given for particular choices of the involved parameters in the solutions to show the evolutionary characteristics.

Similarity reductions and exact solutions for two-dimensional Euler–Boussinesq equations

2019 ◽  
Vol 33 (27) ◽  
pp. 1950328
Author(s):  
En Gui Fan ◽  
Man Wai Yuen
Keyword(s):  
Exact Solutions ◽  
Stream Function ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Similarity Reduction ◽  
Wave Solutions ◽  
Similarity Reductions

In this paper, by introducing a stream function and new coordinates, we transform classical Euler–Boussinesq equations into a vorticity form. We further construct traveling wave solutions and similarity reduction for the vorticity form of Euler–Boussinesq equations. In fact, our similarity reduction provides a kind of linearization transformation of Euler–Boussinesq equations.

scholarly journals New Exponential and Complex Traveling Wave Solutions to the Konopelchenko-Dubrovsky Model

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Faruk Dusunceli
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Ordinary Differential Equation ◽  
Wave Transformation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Parameter Values ◽  
Singular Soliton

The Konopelchenko-Dubrovsky (KD) system is presented by the application of the improved Bernoulli subequation function method (IBSEFM). First, The KD system being Nonlinear partial differential equations system is transformed into nonlinear ordinary differential equation by using a wave transformation. Last, the resulting equation is successfully explored for new explicit exact solutions including singular soliton, kink, and periodic wave solutions. All the obtained solutions in this study satisfy the Konopelchenko-Dubrovsky model. Under suitable choice of the parameter values, interesting two- and three-dimensional graphs of all the obtained solutions are plotted.

Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method

2019 ◽  
Vol 33 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Behzad Ghanbari
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Graphical Interpretation ◽  
Wave Solutions ◽  
Complex Models ◽  
Exponential Rational Function Method

In this paper, some new traveling wave solutions to the Hirota–Maccari equation are constructed with the help of the newly introduced method called generalized exponential rational function method. Several families of exact solutions are found corresponding to the equation. To the best of our knowledge, these solutions are new, and have never been addressed in the literature. The graphical interpretation of the solutions is also depicted. Moreover, it is contemplated that the proposed technique can also be employed to another sort of complex models.

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