Solitary wave solutions of the fourth order Boussinesq equation through the exp(–Ф(η))-expansion method

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.

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On the exact solitary wave solutions to the long-short wave interaction system

ITM Web of Conferences ◽

10.1051/itmconf/20182201063 ◽

2018 ◽

Vol 22 ◽

pp. 01063

Author(s):

Haci Mehmet Baskonus ◽

Tukur Abdulkadir Sulaiman ◽

Hasan Bulut

Keyword(s):

Solitary Wave ◽

Wave Interaction ◽

Expansion Method ◽

Short Wave ◽

Complex Model ◽

Solitary Wave Solutions ◽

Short Transverse ◽

Wave Solutions ◽

Interaction System ◽

2D And 3D

In this paper, the application of the simplified the extended sinh-Gordon equation expansion method to the long-short-wave interaction system. We successfully construct various solitary wave solutions to this nonlinear complex model. The long-short-wave interaction system describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The 2D and 3D surfaces to some of the obtained solutions are plotted.

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Gaussian solitary waves to Boussinesq equation with dual dispersion and logarithmic nonlinearity

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2018.6.8 ◽

2018 ◽

Vol 23 (6) ◽

pp. 942-950 ◽

Cited By ~ 1

Author(s):

Anjan Biswasa ◽

Mehmet Ekici ◽

Abdullah Sonmezoglu

Keyword(s):

Solitary Wave ◽

Shallow Water ◽

Solitary Waves ◽

Water Waves ◽

Trial Function ◽

Boussinesq Equation ◽

Solitary Wave Solutions ◽

Shallow Water Waves ◽

Wave Solutions ◽

Extended Trial

This paper discusses shallow water waves that is modeled with Boussinesq equation that comes with dual dispersion and logarithmic nonlinearity. The extended trial function scheme retrieves exact Gaussian solitary wave solutions to the model.

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

Symmetry ◽

10.3390/sym13112017 ◽

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.

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

Thermal Science ◽

10.2298/tsci160818069j ◽

2017 ◽

Vol 21 (4) ◽

pp. 1783-1788 ◽

Cited By ~ 1

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

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A Generalized Sub-Equation Expansion Method and Some Analytical Solutions to the Inhomogeneous Higher-Order Nonlinear Schrödinger Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2008-1204 ◽

2008 ◽

Vol 63 (12) ◽

pp. 763-777 ◽

Cited By ~ 12

Author(s):

Biao Li ◽

Yong Chen ◽

Yu-Qi Li

Keyword(s):

Solitary Wave ◽

Analytical Solutions ◽

Elliptic Function ◽

Schrodinger Equation ◽

Expansion Method ◽

High Order ◽

Solitary Wave Solutions ◽

Exact Analytical Solutions ◽

Nonlinear Schrödinger ◽

Wave Solutions

On the basis of symbolic computation a generalized sub-equation expansion method is presented for constructing some exact analytical solutions of nonlinear partial differential equations. To illustrate the validity of the method, we investigate the exact analytical solutions of the inhomogeneous high-order nonlinear Schrödinger equation (IHNLSE) including not only the group velocity dispersion, self-phase-modulation, but also various high-order effects, such as the third-order dispersion, self-steepening and self-frequency shift. As a result, a broad class of exact analytical solutions of the IHNLSE are obtained. From our results, many previous solutions of some nonlinear Schrödinger-type equations can be recovered by means of suitable selections of the arbitrary functions and arbitrary constants. With the aid of computer simulation, the abundant structure of bright and dark solitary wave solutions, combined-type solitary wave solutions, dispersion-managed solitary wave solutions, Jacobi elliptic function solutions and Weierstrass elliptic function solutions are shown by some figures.

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