☆ 4.5 Article

Many new exact solutions to the higher-order nonlinear Schrodinger equation with derivative non-Kerr nonlinear terms using three different techniques

OPTIK (2017)

Journal

OPTIK

Volume 143, Issue -, Pages 84-103

Publisher

ELSEVIER GMBH

DOI: 10.1016/j.ijleo.2017.06.025

Keywords

The special kind of (G'/G)-expansion method; phi(6)-Model expansion method; New mapping method; Jacobi elliptic function solutions; Solitons and other solutions; Exact solutions; Higher-order nonlinear Schrodinger equations with derivative non-Kerr nonlinear terms

Categories

Optics

Ask authors/readers for more resources

Protocol

Community support

Reagent

Community support

Abstract

Many new types of Jacobi elliptic function solutions, solitons and other solutions to the higher-order nonlinear Schrodinger equation with derivative non-Kerr nonlinear terms have been found using three mathematical techniques, namely, the special kind of (G'/G)expansion method, the phi(6)-model expansion method and the new mapping method. This equation could be a model equation of pulse propagation beyond ultrashort range in optical communication systems. This model is photonic crystal fiber (PCF). Comparing our new results with the well-known results are given. Also, we compare the results yielding from the three methods with each other. (C) 2017 Elsevier GmbH. All rights reserved.

Authors

I am an author on this paper

Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.5

Not enough ratings

Secondary Ratings

Novelty

-

Significance

-

Scientific rigor

-

Rate this paper

Recommended

Retraction Optics

撤稿声明: The Φ6-model expansion method for solving the Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity

Khalida Bibi

Summary: This paper applies the Phi(6)-model expansion method to derive new exact solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity. The obtained solutions are based on Jacobi elliptic function, hyperbolic function, and trigonometric function solutions. Specific parameter values consistent with constraint conditions are assigned to reveal the dynamic behavior of the solutions.

OPTIK (2021)

Add to Collection

Article Optics

Optical solitons and other solutions for coupled system of nonlinear Biswas-Milovic equation with Kudryashov's law of refractive index by Jacobi elliptic function expansion method

Tarek A. Khalil, Niveen Badra, Hamdy M. Ahmed, Wafaa B. Rabie

Summary: In this article, the Jacobi elliptic function expansion method is used to investigate secure optical soliton solutions in magneto-optic waveguides for a coupled system of the nonlinear Biswas-Milovic equation with Kudryashov's law of refractive index. Bright soliton solutions, dark soliton solutions, and singular-bright combo soliton solutions are obtained, along with periodic solutions and Jacobi elliptic solutions. The most significant achievement of this approach is that it provides all the solutions that cannot be found using other techniques.

OPTIK (2022)

Add to Collection

Article Mathematics, Applied

Optical solitons and other solutions to Kaup-Newell equation with Jacobi elliptic function expansion method

Hamdy M. Ahmed, Wafaa B. Rabie, Maria Alessandra Ragusa

Summary: In this paper, the Kaup-Newell (KN) equation in coupled vector form without four-wave mixing terms in birefringent fibers was studied. Sub-pico-second optical soliton solutions were demonstrated using the Jacobi elliptic function expansion method. In addition to bright and dark solitons, Jacobi elliptic function solutions and hyperbolic solutions were obtained, and graphs for some solutions were presented.

ANALYSIS AND MATHEMATICAL PHYSICS (2021)

Add to Collection

Article Materials Science, Multidisciplinary

Propagation of chirped optical solitons for perturbation higher order nonlinear Schrδdinger equation with dual-power law nonlinearity byΦ6 expansion method

Noha M. Kamel, Hamdy M. Ahmed, Wafaa B. Rabie

Summary: New exact solutions for the perturbation higher order nonlinear Schrödinger equation with dual-power law nonlinearity are investigated using the symbolscript expansion method. Various types of solutions are obtained and the effect of nonlinearity degree on the dynamical behavior of light pulses is analyzed. The study concludes that the dynamical behavior of light pulses is controlled by the nonlinearity degree.

RESULTS IN PHYSICS (2023)

Add to Collection

Article Physics, Applied

Optical spatiotemporal solitary wave solutions of the generalized (3+1)-dimensional Gross-Pitaevskii equation with distributed coefficients

Nilkanta Das, S. Saha Ray

Summary: In this study, the extended Jacobi elliptic function expansion approach was used to analyze a generalized (3+1)-dimensional Gross-Pitaevskii equation with distributed time-dependent coefficients. The approach successfully obtained spatiotemporal soliton solutions and exact extended traveling-wave solutions. Several double periodic, trigonometric, and hyperbolic function solutions were found under specific constraints. The proposed approach is considered to be the most straightforward, efficient, and useful way to handle nonlinear models and generate various exact solutions. The acquired solutions are of considerable importance due to their applicability to a variety of quantum systems.

MODERN PHYSICS LETTERS B (2023)

Add to Collection

Article Mathematics

Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method

Muhammad Shakeel, Attaullah, Mohammed Kbiri Alaoui, Ahmed M. Zidan, Nehad Ali Shah, Wajaree Weera

Summary: This study considers the dispersal caused by the transverse Poisson's effect in a magneto-electro-elastic circular rod using the nonlinear longitudinal wave equation (LWE). The families of solitary wave solutions of the one-dimensional nonlinear LWE are investigated using the generalized exp-function method.

MATHEMATICS (2022)

Add to Collection

Article Materials Science, Multidisciplinary

On closed-form optical solutions to the nonlinear model with the Kerr law nonlinearity

A. Althobaiti, Su Liu, B. Atamuratova, S. Rezaei

Summary: The main contribution of this study is the application of a newly-proposed method to obtain new closed-form optical solutions for the Ginzburg-Landau equation. By employing a wave transformation, the nonlinear model is reduced to an ordinary differential equation. This simple and straightforward technique can be applied to solve non-linear partial differential equations.

RESULTS IN PHYSICS (2023)

Add to Collection

Article Physics, Applied

New optical soliton solutions of fractional perturbed nonlinear Schrodinger equation in nanofibers

S. Saha Ray, N. Das

Summary: This article investigates the space-time fractional perturbed nonlinear Schrodinger equation in nanofibers using the improved tan(phi(xi)/2) expansion method to discover new exact solutions. The obtained soliton solutions are illustrated in 3D graphs to observe their behavior, indicating the proficiency of the proposed method in analyzing nonlinear partial differential models.

MODERN PHYSICS LETTERS B (2022)

Add to Collection

Article Physics, Multidisciplinary

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Aleksandr Tusnin, Alexey Tikan, Kenichi Komagata, Tobias J. Kippenberg

Summary: This paper investigates the application of dissipative Kerr solitons (DKS) based microresonator frequency combs in coupled resonator systems. A model for a one-dimensional lattice of microresonators is derived, and two different dynamical regimes, elliptic and hyperbolic, are identified. Turing patterns, regularized wave collapse, and 2D DKS are studied in these regimes. The study also extends the system to the Su-Schrieffer-Heeger model, showing the dynamics of edge states and edge-bulk interactions initiated by edge-state DKS.

COMMUNICATIONS PHYSICS (2023)

Add to Collection

Article Mathematics, Applied

New solutions for perturbed chiral nonlinear Schrodinger equation

E. S. Aly, Mahmoud A. E. Abdelrahman, S. Bourazza, Abdullah Ali H. Ahmadini, Ahmed Hussein Msmali, Nadia A. Askar

Summary: In this article, stochastic solutions for the perturbed chiral nonlinear Schrodinger equation (PCNLSE) forced by multiplicative noise are extracted using exp[-phi(xi)]-expansion and unified solver methods. These solutions are extremely viable in nonlinear optics, plasma physics, and other applied sciences.

AIMS MATHEMATICS (2022)

Add to Collection

Article Engineering, Mechanical

Exploring lump soliton solutions and wave interactions using new Inverse (G′/G) -expansion approach: applications to the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

Sachin Kumar, Monika Niwas

Summary: In this research article, a new Inverse (G '/G)-Expansion Method is proposed to discover exact soliton solutions for the (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation. Various new soliton solutions for the equation are successfully derived using this method. These results have important applications in multiple fields and are presented through visualizations to demonstrate different characteristics of the soliton solutions.

NONLINEAR DYNAMICS (2023)

Add to Collection

Article Optics

Abundant soliton solutions for Radhakrishnan-Kundu-Laksmanan equation with Kerr law non-linearity by improved tan(Φ(ξ)/2)-expansion technique

Ghazala Akram, Maasoomah Sadaf, Mirfa Dawood

Summary: This paper presents various soliton solutions of the Radhakrishnan-Kundu-Laksmanan (RKL) equation, including hyperbolic, trigonometric, rational, and exponential solutions obtained through an improved tan(Phi(xi)/2)-expansion technique. Graphical illustrations are provided to offer insights into the physical behavior of related phenomena.

OPTIK (2021)

Add to Collection

Article Engineering, Multidisciplinary

Invariant soliton solutions for the coupled nonlinear Schrodinger type equation

Sandeep Malik, Sachin Kumar, Kottakkaran Sooppy Nisar

Summary: This study investigates the optical soliton solutions of nonlinear triple-component Schrodinger equations using the Lie classical approach combined with modified (G'/G)-expansion method and polynomial type assumption. Several explicit solutions including hyperbolic, periodic, and power series solutions are obtained. The stability of one of the reductions is also examined using phase plane theory. Maple software is utilized for graphical representation and verification of the obtained solitons.

ALEXANDRIA ENGINEERING JOURNAL (2023)

Add to Collection

Article Optics

Dark, singular, bright, rational and periodic solutions of the space-time fractional Fokas-Lenells equation by the Φ6-model expansion method

Naila Sajid, Ghazala Akram

Summary: New analytical solutions for the space-time fractional Fokas-Lenells equation with the conformable derivative of order r and s were obtained using the Phi(6)-model expansion method with fractional complex transformation. The physical significance of the geometrical structures for some solutions was discussed for different choices of free parameters.

OPTIK (2021)

Add to Collection

Article Materials Science, Multidisciplinary

Some new type optical and the other soliton solutions of coupled nonlinear Hirota equation

Kottakkaran Sooppy Nisar, Ibrahim E. Inan, H. Yepez-Martinez, Mustafa Inc

Summary: In this study, exact traveling wave solutions of coupled nonlinear Hirota equation (CNHE) were obtained using the generalized (G'/G)-expansion method. The obtained solutions include hyperbolic, trigonometric, and exponential solutions. The analytical results were confirmed through symbolic calculation using Mathematica 11.2. The solutions were illustrated through 3D graphs and 2D plots. The present method has been successfully used to obtain exact traveling wave solutions for various nonlinear partial differential equations.

RESULTS IN PHYSICS (2022)

Add to Collection

Article Engineering, Electrical & Electronic

The φ6-model expansion method for solving the nonlinear conformable time-fractional Schrodinger equation with fourth-order dispersion and parabolic law nonlinearity

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy

OPTICAL AND QUANTUM ELECTRONICS (2018)

Add to Collection

Article Optics

A note on the two papers of Mostafa M. A. Khater et al. and Dianchen Lu et al. [Optik, 158 (2018) 434-450 and 164 (2018) 54-64]

Elsayed M. E. Zayed, Shoukry El-Ganaini, Abdul-Ghani Al-Nowehy, Mohamed E. M. Alngar

OPTIK (2018)

Add to Collection

Editorial Material Physics, Condensed Matter

Comment on the paper of Mostafa M. A. Khater et al. [Superlattices and Microstructures, 113 (2018) 346-358]

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy

SUPERLATTICES AND MICROSTRUCTURES (2018)

Add to Collection

Editorial Material Physics, Condensed Matter

A note on the reply of the manuscript of Aly R. Seadawy et al. [Superlattices and Microstructures, in press]

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mohamed E. M. Aingar, Reham M. A. Shohib

SUPERLATTICES AND MICROSTRUCTURES (2018)

Add to Collection

Article Materials Science, Multidisciplinary

An eerie note of caution from two papers of Mostafa M. A. Khater et al. and Sadaf Bibi et al. [Results in Physics, 7 (2017) 2325-2333 and 4440-4450.]

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Shoukry El-Ganaini, Reham M. A. Shohib

RESULTS IN PHYSICS (2018)

Add to Collection

Article Mathematics, Applied

Solitons and other solutions for higher-order NLS equation and quantum ZK equation using the extended simplest equation method

Elsayed M. E. Zayed, Reham M. A. Shohib, Abdul-Ghani Al-Nowehy

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2018)

Add to Collection

Editorial Material Optics

Reply on comment on four papers of Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham MA Shohib and Khaled AEAlurrfi (Optik 130 (2017) 1295-1311 & Optik 143 (2017) 84-103 & Optik 158 (2018) 970-984 & Optik 144 (2017) 132-148 & Optik 172 (2018) 585-587)

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib, Mohamed E. M. Alngar

OPTIK (2018)

Add to Collection

Article Optics

On solving the nonlinear Schrodinger equation with an anti-cubic nonlinearity in presence of Hamiltonian perturbation terms

Elsayed M. E. Zayed, Mohamed E. M. Alngar, Abdul-Ghani Al-Nowehy

OPTIK (2019)

Add to Collection

Article Physics, Multidisciplinary

New -model expansion method and its applications to the resonant nonlinear Schrodinger equation with parabolic law nonlinearity

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mona E. M. Elshater

EUROPEAN PHYSICAL JOURNAL PLUS (2018)

Add to Collection

Article Engineering, Electrical & Electronic

Comment on the paper of Mostafa M. A. Khater et al. [Optical and Quantum Electronic, 50 (2018) 155]

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib

OPTICAL AND QUANTUM ELECTRONICS (2019)

Add to Collection

Article Mathematics, Applied

On solving the (3+1) -dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method

Elsayed M. E. Zayed, Reham M. A. Shohib, Abdul-Ghani Al-Nowehy

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2019)

Add to Collection

Article Physics, Multidisciplinary

Solitons and other solutions for coupled nonlinear Schrodinger equations using three different techniques

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mona E. M. Elshater

PRAMANA-JOURNAL OF PHYSICS (2019)

Add to Collection

Article Optics

Optical solitons and other solutions to the (2+1)-dimensional coupled system of NLSE by two integration approaches

Elsayed M. E. Zayed, Taher A. Nofal, A. G. Al-Nowehy, Mohamed E. M. Alngar

Summary: Using new mapping approaches and extended auxiliary equation approaches, various solutions of the (2+1)-dimensional coupled nonlinear Schrodinger equations have been obtained, including solitons and other solutions. These solutions describe transverse effects in optical fibers, time-independent corporation, and the field of optical solitons.

OPTIK (2021)

Add to Collection

Article Engineering, Marine

New sub-equation method to construct solitons and other solutions for perturbed nonlinear Schrodinger equation with Kerr law nonlinearity in optical fiber materials

Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib

JOURNAL OF OCEAN ENGINEERING AND SCIENCE (2019)

Add to Collection

Article Mathematics, Applied

On Solving the (2+1)-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau Equation Using Five Different Techniques

Elsayed M. E. Zayed, A. -G Al-Nowehy, Mona E. M. Elshater

JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS (2018)

Add to Collection

No Data Available

© Peeref 2019-2024. All rights reserved.