Kinky breathers, multi-peak and multi-wave soliton solutions for the nonlinear propagation of Kundu–Eckhaus dynamical model

2020 ◽  
Vol 34 (32) ◽  
pp. 2050317
Author(s):  
K. El-Rashidy ◽  
Aly R. Seadawy
Keyword(s):  
Symbolic Computation ◽  
Function Method ◽  
Soliton Solutions ◽  
Logarithmic Transformation ◽  
Nonlinear Propagation ◽  
Dynamical Model ◽  
Wave Method ◽  
Wave Solutions ◽  
Double Exponential

The multi-wave solutions for nonlinear Kundu–Eckhaus (KE) equation are obtained using logarithmic transformation and symbolic computation using the function method. Three-wave method, double exponential and homoclinic breather approach are used to get these solutions. We study the conflict between our results and considerably-known results and state that the solutions reached here are new. By specifying the suitable values for the parameter, the drawings of the solutions obtained are shown in this paper.

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

Investigation of interactional phenomena and multi wave solutions of the quantum hydrodynamic Zakharov–Kuznetsov model

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 91-99
Author(s):  
Khaled El-Rashidy ◽  
Aly R. Seadawy ◽  
Saad Althobaiti ◽  
M. M. Makhlouf
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Transformation Method ◽  
Logarithmic Transformation ◽  
Wave Solutions ◽  
Double Exponential ◽  
Quantum Hydrodynamic ◽  
Parameter Values ◽  
3D Representations

Abstract The symbolic computation with the ansatz function and the logarithmic transformation method are used to obtain a formula for certain exact solutions of the ( 3 + 1 ) \left(3+1) Zakharov–Kuznetsov (Z–K) equation. We use homoclinic breather, three waves method, and double exponential. There is a conflict of results with considerably known results, which indicates the solutions found in this study are new. By selecting appropriate parameter values, 3d representations are plotted to establish W-shaped, multi-peak, and kinky breathers solutions.

scholarly journals Compactons and topological solitons of the Drinfel'd–Sokolov system

2014 ◽  
Vol 19 (2) ◽  
pp. 209-224
Author(s):  
Mustafa Inc ◽  
Eda Fendoglu ◽  
Houria Triki ◽  
Anjan Biswas
Keyword(s):  
Elliptic Function ◽  
Function Method ◽  
Soliton Solutions ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Topological Solitons ◽  
Wave Solutions

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions.

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.

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.

MULTIPLE SOLITON SOLUTIONS FOR THE NAGUMO EQUATION AND THE MODIFIED GENERAL BURGERS-FISHER EQUATION

2006 ◽  
Vol 03 (03) ◽  
pp. 371-381 ◽  
Author(s):  
H. A. ABDUSALAM
Keyword(s):  
Time Delay ◽  
Function Method ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Fisher Equation ◽  
Travelling Wave Solutions ◽  
Limit Case ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Nagumo Equation

A generalized tanh-function method is used for constructing exact travelling wave solutions for Nagumo's equation and the modified generalized Burger-Fisher equation. Also new multiple soliton solutions are obtained for both equations. Limit case of the time delay is studied and the results of the general Burgers-Fisher equations are verified.

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