Solitary wave solutions of (2+1)-dimensional Maccari system

2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid
Keyword(s):  
Nonlinear Optics ◽  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.

scholarly journals New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2017
Author(s):  
Sadullah Bulut ◽  
Mesut Karabacak ◽  
Hijaz Ahmad ◽  
Sameh Askar
Keyword(s):  
Solitary Wave ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Wave Model ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Symmetry Properties

In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the (G′G)-expansion method under Atangana’s definition of β-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of (n+1)-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the β parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

scholarly journals Some Applications of the (G′/G,1/G)-Expansion Method for Finding Exact Traveling Wave Solutions of Nonlinear Fractional Evolution Equations

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 952
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert ◽  
Surattana Sungnul
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Solitary Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

In this paper, the ( G ′ / G , 1 / G ) -expansion method is applied to acquire some new, exact solutions of certain interesting, nonlinear, fractional-order partial differential equations arising in mathematical physics. The considered equations comprise the time-fractional, (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation, and the space-time-fractional generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system in the sense of the conformable fractional derivative. Applying traveling wave transformations to the equations, we obtain the corresponding ordinary differential equations in which each of them provides a system of nonlinear algebraic equations when the method is used. As a result, many analytical exact solutions obtained of these equations are expressed in terms of hyperbolic function solutions, trigonometric function solutions, and rational function solutions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions, solitary wave solutions of kink type, and so on. The method is very efficient, powerful, and reliable for solving the proposed equations and other nonlinear fractional partial differential equations with the aid of a symbolic software package.

scholarly journals New Exact Solutions to the KdV-Burgers-Kuramoto Equation with the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jae-Myoung Kim ◽  
Changbum Chun
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Truncated Painlevé Expansion

Based on the characteristics of the truncated Painlevé expansion method and the Exp-function method, new generalized solitary wave solutions are constructed for the KdV-Burgers-Kuramoto equation, which cannot be directly constructed from the Exp-function method. This work highlights the power of the Exp-function method in providing generalized solitary wave solutions of different physical structures.

scholarly journals Solitary Wave Solutions and Periodic Wave Solutions of theK(m,n)Equation witht-Dependent Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Wei Li
Keyword(s):  
Solitary Wave ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions

The Exp-function method combined withF-expansion method is employed to investigate theK(m,n)equation witht-dependent coefficients. The solitary wave solutions and periodic wave solutions to the equation are constructed analytically under certain circumstances. The results presented in this paper improve the previous results.

The Multiple Exp-Function Method and the Linear Superposition Principle for Solving the (2+1)-Dimensional Calogero–Bogoyavlenskii–Schiff Equation

2015 ◽  
Vol 70 (9) ◽  
pp. 775-779 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Superposition Principle ◽  
Solitary Wave Solutions ◽  
Linear Superposition ◽  
Wave Solutions ◽  
Linear Superposition Principle

AbstractIn this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n-wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.

scholarly journals New exact solutions of the(2+1)-dimensional Broer-Kaup equation by the consistent Riccati expansion method

2017 ◽  
Vol 21 (4) ◽  
pp. 1783-1788 ◽  
Author(s):  
Ying Jiang ◽  
Da-Quan Xian ◽  
Zheng-De Dai
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
High Dimensional ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Linear Waves ◽  
Consistent Riccati Expansion

In this work, we study the (2+1)-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

Numerical soliton solutions of fractional modied (2 + 1)-dimensional Konopelchenko-Dubrovsky equations in plasma physics

2021 ◽  
Author(s):  
Santanu Saha Ray ◽  
B Sagar
Keyword(s):  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Scheme ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Kansa Method

Abstract In this paper, the time-fractional modied (2+1)-dimensional Konopelchenko-Dubrovsky equations have been solved numerically using the Kansa method, in which the multiquadrics used as radial basis function. To achieve this, a numerical scheme based on nite dierenceand Kansa method has been proposed. Also the solitary wave solutions have been obtained by using Kudryashov technique. The computed results are compared with the exact solutions as well as with the soliton solutions obtained by Kudryashov technique to show the accuracy of the proposed method.

scholarly journals The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Integral Method ◽  
First Integral ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type fornandE, the solitary wave solutions of kink-type forEand bell-type forn, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

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