scholarly journals Optical solitons and other soluions for Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

2021 ◽  
Author(s):  
M. Bilal ◽  
Mohammad Youins ◽  
Aly Ramadan Seadawy ◽  
S.T.R. Rizvi
Keyword(s):  
Soliton Solutions ◽  
Periodic Wave ◽  
Computational Technique ◽  
Mixed Complex ◽  
Symbolic Computations ◽  
Significant Relationships ◽  
Wave Solutions ◽  
Component Form ◽  
Contour Plots ◽  
Complex Phenomena

Abstract In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations

Resonance Y-type soliton, hybrid and quasi-periodic wave solutions of a generalized (2+1)-dimensional nonlinear wave equation

2021 ◽  
Author(s):  
Lingchao He ◽  
Jianwen Zhang ◽  
Zhonglong Zhao
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Water Waves ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Before And After

Abstract In this paper, we consider a generalized (2+1)-dimensional nonlinear wave equation. Based on the bilinear, the N-soliton solutions are obtained. The resonance Y-type soliton and the interaction solutions between M-resonance Y-type solitons and P-resonance Y-type solitons are constructed by adding some new constraints to the parameters of the N-soliton solutions. The new type of two-opening resonance Y-type soliton solutions are presented by choosing some appropriate parameters in 3-soliton solutions. The hybrid solutions consisting of resonance Y-type solitons, breathers and lumps are investigated. The trajectories of the lump waves before and after the collision with the Y-type solitons are analyzed from the perspective of mathematical mechanism. Furthermore, the multi-dimensional Riemann-theta function is employed to investigate the quasi-periodic wave solutions. The one-periodic and two-periodic wave solutions are obtained. The asymptotic properties are systematically analyzed, which establish the relations between the quasi-periodic wave solutions and the soliton solutions. The results may be helpful to provide some effective information to analyze the dynamical behaviors of solitons, fluid mechanics, shallow water waves and optical solitons.

Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation

2016 ◽  
Vol 71 (3) ◽  
pp. 235-240 ◽  
Author(s):  
Hengchun Hu ◽  
Xiao Hu ◽  
Bao-Feng Feng
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Cnoidal Wave ◽  
Nonlocal Symmetry ◽  
Nonlocal Symmetries ◽  
Periodic Wave Solutions ◽  
Wave Solutions

AbstractNonlocal symmetries are obtained for the coupled integrable dispersionless (CID) equation. The CID equation is proved to be consistent, tanh-expansion solvable. New, exact interaction excitations such as soliton–cnoidal wave solutions, soliton–periodic wave solutions, and multiple resonant soliton solutions are discussed analytically and shown graphically.

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.

EXACT SOLITON SOLUTIONS AND QUASI-PERIODIC WAVE SOLUTIONS TO THE FORCED VARIABLE-COEFFICIENT KdV EQUATION

2012 ◽  
Vol 26 (19) ◽  
pp. 1250072 ◽  
Author(s):  
YI ZHANG ◽  
ZHILONG CHENG
Keyword(s):  
Variable Coefficient ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Time Dependent ◽  
Bilinear Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Hirota Bilinear ◽  
Exact Soliton Solutions

In this paper, the time-dependent variable-coefficient KdV equation with a forcing term is considered. Based on the Hirota bilinear method, the bilinear form of this equation is obtained, and the multi-soliton solutions are studied. Then the periodic wave solutions are obtained by using Riemann theta function, and it is also shown that classical soliton solutions can be reduced from the periodic wave solutions.

Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms

2020 ◽  
pp. 2150112
Author(s):  
S. U. Rehman ◽  
Aly R. Seadawy ◽  
M. Younis ◽  
S. T. R. Rizvi ◽  
T. A. Sulaiman ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Arbitrary Power ◽  
Non Linear ◽  
Complex Phenomena ◽  
Singular Soliton

In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations.

Highly dispersive optical soliton perturbation with cubic–quintic–septic law via two methods

2021 ◽  
pp. 2150276
Author(s):  
Khalid K. Ali ◽  
Hadi Rezazadeh ◽  
Nauman Raza ◽  
Mustafa Inc
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Optical Solitons ◽  
Optical Soliton ◽  
Mixed Complex ◽  
Solitary Wave Solutions ◽  
Computational System ◽  
Soliton Perturbation ◽  
Wave Solutions

The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena.

scholarly journals Generalized Bilinear Differential Operators Application in a (3+1)-Dimensional Generalized Shallow Water Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jingzhu Wu ◽  
Xiuzhi Xing ◽  
Xianguo Geng
Keyword(s):  
Shallow Water ◽  
Differential Operators ◽  
Shallow Water Equation ◽  
Asymptotic Properties ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solution ◽  
Bell Polynomials ◽  
Periodic Wave Solutions ◽  
Wave Solutions

The relations betweenDp-operators and multidimensional binary Bell polynomials are explored and applied to construct the bilinear forms withDp-operators of nonlinear equations directly and quickly. Exact periodic wave solution of a (3+1)-dimensional generalized shallow water equation is obtained with the help of theDp-operators and a general Riemann theta function in terms of the Hirota method, which illustrate that bilinearDp-operators can provide a method for seeking exact periodic solutions of nonlinear integrable equations. Furthermore, the asymptotic properties of the periodic wave solutions indicate that the soliton solutions can be derived from the periodic wave solutions.

Periodic-wave solutions and asymptotic properties for a (3+1)-dimensional generalized breaking soliton equation in fluids and plasmas

2021 ◽  
pp. 2150344
Author(s):  
Rui-Dong Chen ◽  
Yi-Tian Gao ◽  
Xin Yu ◽  
Ting-Ting Jia ◽  
Gao-Fu Deng ◽  
...  
Keyword(s):  
Asymptotic Properties ◽  
Theta Functions ◽  
Soliton Solutions ◽  
Periodic Wave ◽  
Soliton Equation ◽  
One Dimensional ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Riemann Theta Functions ◽  
The One

In this paper, a (3+1)-dimensional generalized breaking soliton equation is investigated. Based on the one- and two-dimensional Riemann theta functions, one- and two-periodic-wave solutions are derived. We observe that the one-periodic wave is one-dimensional and is viewed as a superposition of the overlapping waves, placed one period apart. With certain parameters, the symmetric feature appears in the two-periodic wave, and the two-periodic wave degenerates to the one-periodic wave. With the series expansions, we explore the relations between the soliton and periodic-wave solutions. According to those relations, asymptotic properties for the periodic-wave solutions to approach to the soliton solutions under certain amplitude conditions are derived.

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