scholarly journals Optical solutions and other solutions for Radhakrishnan-Kundu-Laksmannan equation by using improved modified extended tanh-function method

2021 ◽  
Author(s):  
Ahmed M. Elsherbeny ◽  
Reda El–Barkouky ◽  
Hamdy Ahmed ◽  
Rabab M. I. El-Hassani ◽  
Ahmed H. Arnous
Keyword(s):  
Optical Fiber ◽  
Function Method ◽  
Pulse Propagation ◽  
Periodic Wave ◽  
Optical Fiber Communications ◽  
Periodic Wave Solutions ◽  
Bright Solitons ◽  
Wave Solutions ◽  
Elliptic Solutions ◽  
Fiber Communications

Abstract This paper studies Radhakrishnan-Kundu-Laksmannan equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh-function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically.

Instability modulation properties of the (2 + 1)-dimensional Kundu–Mukherjee–Naskar model in travelling wave solutions

2021 ◽  
pp. 2150217
Author(s):  
Haci Mehmet Baskonus ◽  
Juan Luis García Guirao ◽  
Ajay Kumar ◽  
Fernando S. Vidal Causanilles ◽  
German Rodriguez Bermudez
Keyword(s):  
Function Method ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Validity Of Results ◽  
Periodic Wave Solutions ◽  
Wave Solutions

This paper focuses on the instability modulation and new travelling wave solutions of the (2 + 1)-dimensional Kundu–Mukherjee–Naskar equation via the tanh function method. Dark, mixed dark–bright, complex solitons and periodic wave solutions are archived. Strain conditions for the validity of results are also reported. Instability modulation properties of the governing model are also extracted. Various wave simulations in 2D, 3D and contour graphs under the strain conditions are presented.

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.

New periodic wave solutions via Exp-function method

2008 ◽  
Vol 372 (6) ◽  
pp. 830-840 ◽  
Author(s):  
S.A. El-Wakil ◽  
M.A. Abdou ◽  
A. Hendi
Keyword(s):  
Function Method ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions

Soliton Solution, Bäcklund Transformation, and Conservation Laws for the Sasa-Satsuma Equation in the Optical Fiber Communications

2010 ◽  
Vol 65 (4) ◽  
pp. 291-300 ◽  
Author(s):  
Ying Liu ◽  
Yi-Tian Gao ◽  
Tao Xu ◽  
Xing Lü ◽  
Zhi-Yuan Sun ◽  
...  
Keyword(s):  
Optical Fiber ◽  
Conservation Laws ◽  
Soliton Solution ◽  
Pulse Propagation ◽  
Bäcklund Transformation ◽  
Fourier Method ◽  
Lax Pair ◽  
Optical Fiber Communications ◽  
Backlund Transformation ◽  
Fiber Communications

Under investigation in this paper, with symbolic computation, is the Sasa-Satsuma (SS) equation which can describe the propagation of ultra short pulses in optical fiber communications. By virtue of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair for the SS equation is directly established. Based on such a Lax pair, a Bäcklund transformation is constructed, through which the explicit onesoliton solution is derived.Meanwhile, an infinite number of conservation laws is provided to indicate the integrability of the SS equation in the Liouville sense. To further understand the stability of the one-soliton solution, we employ the split-step Fourier method to simulate the propagation of the soliton pulses under the finite initial perturbations. In addition, the interaction of two adjacent pulses with different separation distances is investigated through numerical simulation. Analytic and numerical results discussed in this paper are expected to be applied to the description of the optical pulse propagation.

Exact Traveling Wave Solutions for the Modified Kawahara Equation

2005 ◽  
Vol 60 (3) ◽  
pp. 139-144 ◽  
Author(s):  
Ahmed Elgarayhi
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Mapping Method ◽  
Rational Solutions ◽  
Kawahara Equation ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Elliptic Solutions

The mapping method is used with the aid of the symbolic computation system Mathematica for constructing exact solutions of the modified Kawahara equation. By this method the modified Kawahara equation is investigated and new exact traveling wave solutions are obtained. The solutions obtained in this paper include Jacobi elliptic solutions, combined Jacobi elliptic solutions, solitary wave solutions, periodic wave solutions, trigonometric solutions and rational solutions.

scholarly journals Solitary Wave Solutions and Periodic Wave Solutions of theK(m,n)Equation witht-Dependent Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Wei Li
Keyword(s):  
Solitary Wave ◽  
Function Method ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions

The Exp-function method combined withF-expansion method is employed to investigate theK(m,n)equation witht-dependent coefficients. The solitary wave solutions and periodic wave solutions to the equation are constructed analytically under certain circumstances. The results presented in this paper improve the previous results.

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