Traveling wave solutions for Burgers-Sharma-Tasso-Olver equation with variable coefficients: the improved tanh-coth method vs. exp. function method

2017 ◽  
Vol 11 ◽  
pp. 825-831
Author(s):  
Cesar A. Gomez S. ◽  
Juan C. Hernandez
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Variable Coefficients ◽  
Wave Solutions

THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS

2012 ◽  
Vol 22 (05) ◽  
pp. 1250126 ◽  
Author(s):  
FANG YAN ◽  
CUNCAI HUA ◽  
HAIHONG LIU ◽  
ZENGRONG LIU
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Analytic Solutions ◽  
Auxiliary Function ◽  
Kp Equation ◽  
Gardner Equation ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kp Equations

By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

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.

EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2010 ◽  
Vol 24 (10) ◽  
pp. 1011-1021 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL ◽  
LUWAI WAZZAN
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Higher Dimensional

The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh–coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.

scholarly journals New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hasibun Naher ◽  
Farah Aini Abdullah ◽  
M. Ali Akbar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solutions ◽  
Traveling Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equation ◽  
Traveling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions ◽  
Higher Dimensional

We construct new analytical solutions of the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

scholarly journals New non-traveling wave solutions for (3+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

2021 ◽  
Vol 6 (3) ◽  
pp. 2996-3008
Author(s):  
Yuanqing Xu ◽  
◽  
Xiaoxiao Zheng ◽  
Jie Xin ◽  
◽  
...  
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Variable Coefficients ◽  
Wave Solutions ◽  
Dimensional Variable

An analytical method for soliton solutions of perturbed Schrödinger’s equation with quadratic-cubic nonlinearity

2019 ◽  
Vol 33 (03) ◽  
pp. 1950018 ◽  
Author(s):  
Behzad Ghanbari ◽  
Nauman Raza
Keyword(s):  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Cubic Nonlinearity ◽  
Nonlinear Media ◽  
Schrödinger’S Equation ◽  
Wave Solutions ◽  
First Time ◽  
Schrödinger's Equation

In this study, we acquire some new exact traveling wave solutions to the nonlinear Schrödinger’s equation in the presence of Hamiltonian perturbations. The compendious integration tool, generalized exponential rational function method (GERFM), is utilized in the presence of quadratic-cubic nonlinear media. The obtained results depict the efficiency of the proposed scheme and are being reported for the first time.

Multiple wave solutions for nonlinear burgers equations using the multiple exp-function method

2021 ◽  
pp. 2150149
Author(s):  
Khaled A. Gepreel ◽  
E. M. E. Zayed
Keyword(s):  
Traveling Wave ◽  
Software Package ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Multiple Wave ◽  
Wave Solutions ◽  
The One

In this paper, we use the multiple exp-function method to explicity present traveling wave solutions, double-traveling wave (DTW) solutions and triple-traveling wave solutions (TWs) which include one-soliton, double-soliton and triple-soliton solutions for nonlinear partial differential equations (NPDEs) via, the (2+1)-dimensional and (3+1)-dimensional nonlinear Burgers PDEs in mathematical physics. In this work, we build some series of straightforward and new solutions successfully with the help of a computerized symbol computational software package like Maple or Mathematica. We will make some drawings in some cases with specific values for the relevant parameters for each obtained solutions such as the one-traveling wave solutions, double-traveling wave solutions and TWs. This method is efficient and powerful in solving a wide class of NPDEs.

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