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.

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.

New traveling wave solutions of the perturbed nonlinear Schrödingers equation in the left-handed metamaterials

2018 ◽  
Vol 13 (01) ◽  
pp. 2050022 ◽  
Author(s):  
Alphonse Houwe ◽  
Mibaile Justin ◽  
Serge Y. Doka ◽  
Kofane Timoleon Crepin
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Fiber Optic ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Simple Equation ◽  
Left Handed ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This paper extracts the analytical soliton solutions of the perturbed NLSE given in (1). We use successfully two integration methods namely the extended simple equation method and generalized Kudryashov method. In view of the results obtained, some new additional ones have been obtained. The results are dark, bright and exact solutions that propagate in the fiber optic and left-handed metamaterials (LHMs).

scholarly journals Traveling Wave Solutions of Nonlinear Evolution Equation via Enhanced(G’/G)- Expansion Method

2014 ◽  
Vol 33 ◽  
pp. 83-92 ◽  
Author(s):  
Md. Ekramul Islam ◽  
Kamruzzaman Khan ◽  
M Ali Akbar ◽  
Rafiqul Islam
Keyword(s):  
Rational Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Wave Solutions

In this article, the Enhanced (G'/G)-expansion method has been projected to find the traveling wave solutions for nonlinear evolution equations(NLEEs) via the (2+1)-dimensional Burgers equation. The efficiency of this method for finding these exact solutions has been demonstrated with the help of symbolic computation software Maple. By this method we have obtained many new types of complexiton soliton solutions, such as, various combinations of trigonometric periodic function and rational function solutions, various combination of hyperbolic function and rational function solutions. The proposed method is direct, concise and effective, and can be used for many other nonlinear evolution equations. GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 83-92 DOI: http://dx.doi.org/10.3329/ganit.v33i0.17662

Data Processing in Abound Solutions of (2 + 1)-dimensional Boussinesq Equation

2014 ◽  
Vol 1056 ◽  
pp. 215-220
Author(s):  
Han Kun Gong ◽  
Xiao Shan Zhao ◽  
Guan Hua Zhao
Keyword(s):  
Data Processing ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Function Method ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, the repeated exp-function method is applied to construct exact traveling wave solutions of the (2+1)-dimensional Boussinesq equation. With aid of symbolic computation, many generalized solitary solutions, periodic solutions and other exact solutions are successfully obtained. Thus, it is proved that the method is straightforward and effective to solve the nonlinear evolutions equations.

scholarly journals Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Cesar A. Gómez S ◽  
Alvaro H. Salas ◽  
Bernardo Acevedo Frias
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Point Of View ◽  
Computational Method ◽  
New Approach ◽  
Wave Solutions ◽  
Projective Riccati Equation Method ◽  
Kdv6 Equation

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.

scholarly journals Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type forK(m,n)Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Xianbin Wu ◽  
Weiguo Rui ◽  
Xiaochun Hong
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the integral bifurcation method, we study the nonlinearK(m,n)equation for all possible values ofmandn. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions ofK(n,n),K(2n−1,n),K(3n−2,n),K(4n−3,n), andK(m,1)equations are chosen to illustrate with the concrete features.

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