Soliton wave solutions in optical metamaterials with anti-cubic law of nonlinearity by ITEM

Optik ◽  
2018 ◽  
Vol 164 ◽  
pp. 371-379 ◽  
Author(s):  
Mohammadreza Foroutan ◽  
Jalil Manafian ◽  
Isa Zamanpour
Keyword(s):  
Optical Metamaterials ◽  
Wave Solutions ◽  
Cubic Law ◽  
Soliton Wave Solutions

Analytical new soliton wave solutions of the nonlinear conformable time-fractional coupled Whitham–Broer–Kaup equations

2021 ◽  
pp. 2150492
Author(s):  
Delmar Sherriffe ◽  
Diptiranjan Behera ◽  
P. Nagarani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Function Method ◽  
Visual Representations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Varying Parameters ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The study of nonlinear physical and abstract systems is greatly important in order to determine the behavior of the solutions for Fractional Partial Differential Equations (FPDEs). In this paper, we study the analytical wave solutions of the time-fractional coupled Whitham–Broer–Kaup (WBK) equations under the meaning of conformal fractional derivative. These solutions are derived using the modified extended tanh-function method. Accordingly, different new forms of the solutions are obtained. In order to understand its behavior under varying parameters, we give the visual representations of all the solutions. Finally, the graphs are discussed and a conclusion is given.

Multiple rogue and soliton wave solutions to the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation arising in fluid mechanics and plasma physics

2021 ◽  
pp. 2150383
Author(s):  
Onur Alp Ilhan ◽  
Sadiq Taha Abdulazeez ◽  
Jalil Manafian ◽  
Hooshmand Azizi ◽  
Subhiya M. Zeynalli
Keyword(s):  
Rogue Wave ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
The Novel ◽  
Algebraic Equations ◽  
Bilinear Method ◽  
Dynamical Characteristics ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Soliton Wave Solutions

Under investigation in this paper is the generalized Konopelchenko–Dubrovsky–Kaup-Kupershmidt equation. Based on bilinear method, the multiple rogue wave (RW) solutions and the novel multiple soliton solutions are constructed by giving some specific activation functions for the considered model. By means of symbolic computation, these analytical solutions and corresponding rogue wave solutions are obtained via Maple 18 software. The exact lump and RW solutions, by solving the under-determined nonlinear system of algebraic equations for the specified parameters, will be constructed. Via various three-dimensional plots and density plots, dynamical characteristics of these waves are exhibited.

Lump soliton wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equation and KdV equation

2019 ◽  
Vol 33 (18) ◽  
pp. 1950199 ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Raghda A. M. Attia
Keyword(s):  
Kdv Equation ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
Wave Solutions ◽  
All Solutions ◽  
Long Range Interactions ◽  
Weak Scattering ◽  
Novel Method ◽  
Soliton Wave Solutions

This paper studies (2+1)-dimensional Konopelchenko–Dubrovsky equation and (2+1)-dimensional KdV equation via a modified auxiliary equation technique. These two systems describe the connection between the nonlinear weaves with a weak scattering and long-range interactions between the tropical, mid-latitude troposphere, the interaction of equatorial and mid-latitude Rossby waves, respectively. We implement a novel technique to these systems to find analytical traveling wave solutions. The performance of this novel method shows its ability for applying on various nonlinear partial differential equations. All solutions obtained are checked by the Maple software system and verified for its high fidelity.

Smooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems: Two Models

2019 ◽  
Vol 29 (04) ◽  
pp. 1950047
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Shengfu Deng
Keyword(s):  
Traveling Wave ◽  
Singular System ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Regular System ◽  
Wave System ◽  
Optical Metamaterials ◽  
Wave Solutions ◽  
Straight Line ◽  
Kink Wave

For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green–Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions.

Traveling Wave Solutions in Optical Metamaterials Equation

2017 ◽  
Vol 17 (1) ◽  
pp. 123-141 ◽  
Author(s):  
Yueling Cheng ◽  
Dianchen Lu ◽  
Yuhai Wu ◽  
Jiangbo Zhou ◽  
Linjun Wang
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Optical Metamaterials ◽  
Wave Solutions

scholarly journals Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity

2019 ◽  
Vol 8 (1) ◽  
pp. 559-567 ◽  
Author(s):  
M.S. Osman ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami
Keyword(s):  
Applied Sciences ◽  
Power Law ◽  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Mathematical Tool ◽  
Rational Solutions ◽  
Wave Solutions ◽  
The Unified Method ◽  
Soliton Wave Solutions ◽  
Unified Method

Abstract In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

Cubic–quartic solitons in couplers with optical metamaterials having quadratic–cubic law of nonlinearity

Optik ◽  
2021 ◽  
pp. 168065
Author(s):  
Elsayed M.E. Zayed ◽  
Mohamed E.M. Alngar ◽  
Reham M.A. Shohib ◽  
Anjan Biswas ◽  
Salam Khan ◽  
...  
Keyword(s):  
Optical Metamaterials ◽  
Cubic Law
Sign in / Sign up

Export Citation Format

Share Document