New Jacobi elliptic solutions and other solutions with quadratic-cubic nonlinearity using two mathematical methods

2018 ◽  
Vol 13 (02) ◽  
pp. 2050043 ◽  
Author(s):  
Savaissou Nestor ◽  
Mibaile Justin ◽  
Douvagai ◽  
Gambo Betchewe ◽  
Serge Y. Doka ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Higher Order ◽  
Auxiliary Equation ◽  
Cubic Nonlinearity ◽  
Mathematical Methods ◽  
Auxiliary Equation Method ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Elliptic Solutions

In this paper, we apply two powerful methods, namely, the new extended auxiliary equation method and the generalized Kudryashov method for constructing many exact solutions and other solutions for the higher order dispersive nonlinear Schrödinger’s equation to secure soliton solutions in quadratic-cubic medium. Various solutions of the resulting nonlinear ODE are obtained by using the above two methods.

scholarly journals Investigation of Dark and Bright Soliton Solutions of Some Nonlinear Evolution Equations

2018 ◽  
Vol 22 ◽  
pp. 01056 ◽  
Author(s):  
Seyma Tuluce Demiray ◽  
Hasan Bulut
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Nonlinear Evolution Equations ◽  
Bright Soliton ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Ostrovsky Equation

In this paper, generalized Kudryashov method (GKM) is used to find the exact solutions of (1+1) dimensional nonlinear Ostrovsky equation and (4+1) dimensional Fokas equation. Firstly, we get dark and bright soliton solutions of these equations using GKM. Then, we remark the results we found using this method.

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 Exact Solutions for a Generalized KdV-MKdV Equation with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Bo Tang ◽  
Xuemin Wang ◽  
Yingzhe Fan ◽  
Junfeng Qu
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mkdv Equation ◽  
Variable Coefficients ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Mathematical Tool ◽  
Auxiliary Equation Method

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of variable-coefficient KdV-MKdV equation. As a result, more new exact nontravelling solutions, which include soliton solutions, combined soliton solutions, triangular periodic solutions, Jacobi elliptic function solutions, and combined Jacobi elliptic function solutions, for the KdV-MKdV equation are obtained. It is shown that the considered method provides a very effective, convenient, and powerful mathematical tool for solving many other nonlinear partial differential equations with variable coefficients in mathematical physics.

scholarly journals Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 369
Author(s):  
S. Abbagari ◽  
A. Houwe ◽  
H. Rezazadeh ◽  
A. Bekir ◽  
S. Y. Doka
Keyword(s):  
Optical Fibers ◽  
Coupling Coefficient ◽  
Soliton Solutions ◽  
Kerr Nonlinearity ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Mathematical Methods ◽  
Auxiliary Equation Method ◽  
Equivalent Equation ◽  
Intermodal Dispersion

In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.

scholarly journals Infinitely Many Elliptic Solutions to a Simple Equation and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Long Wei ◽  
Yang Wang
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Simple Equation ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Jacobi Elliptic Function ◽  
Auxiliary Equation Method ◽  
Elliptic Solutions

Based on auxiliary equation method and Bäcklund transformations, we present an idea to find infinitely many Weierstrass and Jacobi elliptic function solutions to some nonlinear problems. First, we give some nonlinear iterated formulae of solutions and some elliptic function solutions to a simple auxiliary equation, which results in infinitely many Weierstrass and Jacobi elliptic function solutions of the simple equation. Then applying auxiliary equation method to some nonlinear problems and combining the results with exact solutions of the auxiliary equation, we obtain infinitely many elliptic function solutions to the corresponding nonlinear problems. The employed approach is powerful and can be also applied to solve other nonlinear differential equations.

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

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