Non-traveling Wave Exact Solutions of (3+1)-Dimensional Yu-Toda-Sasa-Fukuyama Equation

2017 ◽  
pp. 373-384
Author(s):  
Najva Aminakbari ◽  
Guo-qiang Dang ◽  
Yong-yi Gu ◽  
Wen-jun Yuan
Keyword(s):  
Exact Solutions ◽  
Traveling Wave

scholarly journals On the Exact Solutions of Two (3+1)-Dimensional Nonlinear Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanning Meng ◽  
Yongyi Gu
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Shallow Water ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Complex Method ◽  
Meromorphic Solutions ◽  
Complex Differential Equations ◽  
Bkp Equation

In this article, exact solutions of two (3+1)-dimensional nonlinear differential equations are derived by using the complex method. We change the (3+1)-dimensional B-type Kadomtsev-Petviashvili (BKP) equation and generalized shallow water (gSW) equation into the complex differential equations by applying traveling wave transform and show that meromorphic solutions of these complex differential equations belong to class W, and then, we get exact solutions of these two (3+1)-dimensional equations.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

scholarly journals The first integral method and traveling wave solutions to Davey–Stewartson equation

2012 ◽  
Vol 17 (2) ◽  
pp. 182-193 ◽  
Author(s):  
Hossein Jafari ◽  
Atefe Sooraki ◽  
Yahya Talebi ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integral Method ◽  
Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

Bifurcations and Exact Solutions for a Class of MKdV Equations with the Conformable Fractional Derivative via Dynamical System Method

2020 ◽  
Vol 30 (01) ◽  
pp. 2050004 ◽  
Author(s):  
Jianli Liang ◽  
Longkun Tang ◽  
Yonghui Xia ◽  
Yi Zhang
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Order ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Leibniz Rule ◽  
Wave Transformation ◽  
Conformable Fractional Derivative ◽  
Simplest Equation Method

In 2014, Khalil et al. [2014] proposed the conformable fractional derivative, which obeys chain rule and the Leibniz rule. In this paper, motivated by the monograph of Jibin Li [Li, 2013], we study the exact traveling wave solutions for a class of third-order MKdV equations with the conformable fractional derivative. Our approach is based on the bifurcation theory of planar dynamical systems, which is much different from the simplest equation method proposed in [Chen & Jiang, 2018]. By employing the traveling wave transformation [Formula: see text] [Formula: see text], we reduce the PDE to an ODE which depends on the fractional order [Formula: see text], then the analysis depends on the order [Formula: see text]. Moreover, as [Formula: see text], the exact solutions are consistent with the integer PDE. However, in all the existing papers, the reduced ODE is independent of the fractional order [Formula: see text]. It is believed that this method can be applicable to solve the other nonlinear differential equations with the conformable fractional derivative.

scholarly journals Approximate Traveling Wave Solutions of Coupled Whitham-Broer-Kaup Shallow Water Equations by Homotopy Analysis Method

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
M. M. Rashidi ◽  
D. D. Ganji ◽  
S. Dinarvand
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Homotopy Analysis Method ◽  
Shallow Water Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Analysis Method ◽  
Wave Solutions ◽  
Homotopy Analysis

The homotopy analysis method (HAM) is applied to obtain the approximate traveling wave solutions of the coupled Whitham-Broer-Kaup (WBK) equations in shallow water. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the systems of nonlinear partial differential equations.

scholarly journals An effective technique for the conformable space-time fractional EW and modified EW equations

2019 ◽  
Vol 8 (1) ◽  
pp. 157-163 ◽  
Author(s):  
K. Hosseini ◽  
A. Bekir ◽  
F. Rabiei
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Ordinary Differential Equations ◽  
Traveling Wave ◽  
Expansion Method ◽  
Space Time ◽  
Wave Transformation ◽  
Nonlinear Ordinary Differential Equations ◽  
Effective Technique ◽  
Fractional Models

AbstractThe current work deals with the fractional forms of EW and modified EW equations in the conformable sense and their exact solutions. In this respect, by utilizing a traveling wave transformation, the governing space-time fractional models are converted to the nonlinear ordinary differential equations (NLODEs); and then, the resulting NLODEs are solved through an effective method called the exp(−ϕ(ϵ))-expansion method. As a consequence, a number of exact solutions to the fractional forms of EW and modified EW equations are generated.

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.

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.

HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS

2011 ◽  
Vol 21 (02) ◽  
pp. 527-543 ◽  
Author(s):  
JIBIN LI ◽  
YI ZHANG
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Wave Equations ◽  
Periodic Wave ◽  
Nonlinear Wave Equations ◽  
Center Manifolds ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Gap Soliton ◽  
Hyperbolic Equilibrium

For the Lax KdV5 equation and the KdV–Sawada–Kotera–Ramani equation, their corresponding four-dimensional traveling wave systems are studied by using Congrove's method. Exact explicit gap soliton, embedded soliton, periodic and quasi-periodic wave solutions are obtained. The existence of homoclinic manifolds to three kinds of equilibria including a hyperbolic equilibrium, a center-saddle and an equilibrium with zero pair of eigenvalues is revealed. The bifurcation conditions of equilibria are given.

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