Extraction of optical solitons in birefringent fibers for Biswas-Arshed equation via extended trial equation method

Abstract This article obtains optical solitons to the Biswas-Arshed equation for birefringent fibers with higher order dispersions and in the absence of four-wave mixing terms, in a media with Kerr type nonlinearity. Optical dark, singular and bright soliton solutions are articulated by applying an imaginative integration technique, the extended trial equation scheme. Various additional traveling wave solutions are produced with this integration technique, which include rational solutions, Jacobi elliptic function solutions and periodic singular solutions. From the mathematical analysis some constraints are recognized that ensure the actuality of solitons.

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Optical solitons for paraxial wave equation in Kerr media

Modern Physics Letters B ◽

10.1142/s0217984919500209 ◽

2019 ◽

Vol 33 (03) ◽

pp. 1950020 ◽

Cited By ~ 12

Author(s):

Kashif Ali ◽

Syed Tahir Raza Rizvi ◽

Badar Nawaz ◽

Muhammad Younis

Keyword(s):

Wave Equation ◽

Schrodinger Equation ◽

Soliton Solutions ◽

Optical Solitons ◽

Equation Method ◽

Kerr Media ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Paraxial Wave Equation ◽

Extended Trial

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

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Optical solitons in birefringent fibers with weak non-local nonlinearity and four-wave mixing by extended trial equation method

Optik ◽

10.1016/j.ijleo.2018.04.010 ◽

2018 ◽

Vol 166 ◽

pp. 285-293 ◽

Cited By ~ 2

Author(s):

Anjan Biswas ◽

Mehmet Ekici ◽

Abdullah Sonmezoglu ◽

M.M. Babatin

Keyword(s):

Four Wave Mixing ◽

Optical Solitons ◽

Equation Method ◽

Wave Mixing ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Non Local ◽

Local Nonlinearity ◽

Extended Trial

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OPTICAL SOLITONS IN BIREFRINGENT FIBERS WITH FOUR{WAVE MIXING BY EXTENDED TRIAL EQUATION METHOD

Scientia Iranica ◽

10.24200/sci.2018.21144 ◽

2018 ◽

Vol 0 (0) ◽

pp. 0-0

Author(s):

Anjan Biswas ◽

Mehmet Ekici ◽

Abdullah Sonmezoglu ◽

Qin Zhou ◽

Seithuti P. Moshokoa ◽

...

Keyword(s):

Four Wave Mixing ◽

Optical Solitons ◽

Equation Method ◽

Wave Mixing ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Extended Trial

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Chirped and chirp-free optical solitons for Heisenberg ferromagnetic spin chains model

Modern Physics Letters B ◽

10.1142/s0217984921501396 ◽

2021 ◽

pp. 2150139

Author(s):

Syed Tahir Raza Rizvi ◽

Aly R. Seadawy ◽

Ishrat Bibi ◽

Muhammad Younis

Keyword(s):

Graphical Representation ◽

Spin Dynamics ◽

Soliton Solutions ◽

Elliptic Functions ◽

Optical Solitons ◽

Spin Chains ◽

Solitary Wave Solutions ◽

Rational Solutions ◽

Wave Solutions ◽

Ode Method

In this paper, we study (2+1)-dimensional non-linear spin dynamics of Heisenberg ferromagnetic spin chains equation (HFSCE) for various soliton solutions. We obtain two types of optical solitons i.e. chirp free and chirped solitons. We obtain bright and bright-like soliton, singular-like solitons, periodic and rational solutions, Weierstrass elliptic functions solutions and other solitary wave solutions for HFSCE with the aid of sub-ODE method. At the end, we present graphical representation of our solutions.

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Optical solitons in DWDM system by extended trial equation method

Optik ◽

10.1016/j.ijleo.2017.05.057 ◽

2017 ◽

Vol 141 ◽

pp. 157-167 ◽

Cited By ~ 48

Author(s):

Mehmet Ekici ◽

Abdullah Sonmezoglu ◽

Qin Zhou ◽

Anjan Biswas ◽

Malik Zaka Ullah ◽

...

Keyword(s):

Optical Solitons ◽

Equation Method ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Dwdm System ◽

Extended Trial

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Dynamics of optical solitons incorporating Kerr dispersion and self-frequency shift

Modern Physics Letters B ◽

10.1142/s0217984919502208 ◽

2019 ◽

Vol 33 (19) ◽

pp. 1950220

Author(s):

Asma Rashid Butt ◽

Muhammad Abdullah ◽

Nauman Raza

Keyword(s):

Frequency Shift ◽

Optical Fibers ◽

Laser Light ◽

Soliton Solutions ◽

Dark Soliton ◽

Optical Solitons ◽

Light Pulses ◽

Ode Method ◽

Analytical Approaches ◽

Extended Trial

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons.

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EXACT TRAVELING WAVE SOLUTIONS OF A HIGHER-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

Modern Physics Letters B ◽

10.1142/s0217984910023062 ◽

2010 ◽

Vol 24 (10) ◽

pp. 1011-1021 ◽

Cited By ~ 25

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.

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Extended Trial Equation Method for Nonlinear Partial Differential Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2014-0345 ◽

2015 ◽

Vol 70 (4) ◽

pp. 269-279 ◽

Cited By ~ 14

Author(s):

Khaled A. Gepreel ◽

Taher A. Nofal

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Nonlinear Partial Differential Equations ◽

Equation Method ◽

Hyperbolic Function ◽

Jacobi Elliptic Function ◽

Partial Differential ◽

Extended Trial Equation Method ◽

Trial Equation Method ◽

Extended Trial

AbstractThe main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber–Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

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