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.

OPTICAL SOLITON SOLUTIONS OF THE LONG-SHORT-WAVE INTERACTION SYSTEM

2013 ◽  
Vol 22 (02) ◽  
pp. 1350015 ◽  
Author(s):  
AHMET BEKIR ◽  
ESIN AKSOY ◽  
ÖZKAN GÜNER
Keyword(s):  
Soliton Solution ◽  
Function Method ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Short Wave ◽  
Optical Soliton ◽  
Physical Parameters ◽  
Ansatz Method ◽  
Topological Soliton ◽  
Dependent Model

This paper, studies the long-short-wave interaction (LS) equation. An optical soliton solution is obtained by the exp-function method and the ansatz method. Subsequently, we formally derive the dark (topological) soliton solutions for this equation. By using the exp-function method, some additional solutions will be derived. The physical parameters in the soliton solutions of ansatz method: amplitude, inverse width, and velocity are obtained as functions of the dependent model coefficients.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

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.

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.

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

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 Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Abdelfattah El Achab
Keyword(s):  
Wave Equation ◽  
Elliptic Function ◽  
Function Method ◽  
Boussinesq Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Weierstrass Elliptic Function ◽  
Wave Solutions ◽  
Generalized Boussinesq Equation

Travelling wave solutions for the generalized Boussinesq wave equation are studied by using the Weierstrass elliptic function method. As a result, some previously known solutions are recovered, and at the same time some new ones are also given, as well as integrable ones.

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.

Dispersive soliton solutions for the Salerno equation for the nonlinear discrete electrical lattice in the forbidden bandgaps

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El-Barkouky ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
Rabab M. I. El-Hassani ◽  
...  
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional ◽  
Bright Solitons ◽  
Jacobi Elliptic Function Method

In this paper, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear discrete electrical lattice in the forbidden bandgaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, three-dimensional and two-dimensional graphs are presented.

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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