SPATIAL XPM-PAIRED SOLITONS IN NONLINEAR METAMATERIALS

We investigate spatial XPM-paired solitons in nonlinear metamaterials (MMs) based on the (1 + 1)-dimensional coupled nonlinear Schrodinger equation (NLSE) describing the co-propagation of two optical beams of different frequencies in the MM with a Kerr-type nonlinear polarization. Three types of XPM-paired solitons including bright-bright, bright-dark and dark-dark solitons for different combination of the signs of refractive index experienced by the two beams, respectively, are obtained by using a generalized hyperbolic function method, which makes the temporal XPM-paired solitons in optical fibers find their spatial counterparts in MMs. Numerical simulations are performed to confirm the theoretical predictions and further identify the propagation properties of the spatial XPM-paired solitons in MMs described by Drude model.

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The conformable space–time fractional Fokas–Lenells equation and its optical soliton solutions based on three analytical schemes

International Journal of Modern Physics B ◽

10.1142/s0217979221500041 ◽

2020 ◽

pp. 2150004

Author(s):

Asim Zafar ◽

Muhammad Raheel ◽

Ahmet Bekir ◽

Waseem Razzaq

Keyword(s):

Optical Fibers ◽

Function Method ◽

Pulse Propagation ◽

Soliton Solutions ◽

Space Time ◽

Hyperbolic Function ◽

Nonlinear Wave Propagation ◽

Different Types ◽

Hyperbolic Function Method ◽

Exact Soliton Solutions

This paper is about the study of space–time fractional Fokas–Lenells equation that describes nonlinear wave propagation in optical fibers. Three prominent schemes are employed for extracting different types of exact soliton solutions. In particular, the [Formula: see text] function method, the hyperbolic function method and the simplest Riccati equation scheme are investigated for the said model. As a sequel, a series of soliton solutions are obtained and verified through MATHEMATICA. The obtained solutions are significant additions in some specific fields of physics and engineering. Furthermore, the 3D graphical descriptions are left to analyze the pulse propagation for the reader.

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A modified hyperbolic function method and its application to the Toda lattice

Applied Mathematics and Computation ◽

10.1016/j.amc.2005.02.036 ◽

2006 ◽

Vol 172 (2) ◽

pp. 938-945 ◽

Cited By ~ 2

Author(s):

Hongyan Zhi ◽

Xueqin Zhao ◽

Zhongyuan Yang ◽

Hongqing Zhang

Keyword(s):

Function Method ◽

Toda Lattice ◽

Hyperbolic Function ◽

Hyperbolic Function Method

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Complex hyperbolic-function method and its applications to nonlinear equations

Physics Letters A ◽

10.1016/j.physleta.2006.01.094 ◽

2006 ◽

Vol 355 (1) ◽

pp. 32-38 ◽

Cited By ~ 12

Author(s):

Cheng-Lin Bai ◽

Hong Zhao

Keyword(s):

Nonlinear Equations ◽

Function Method ◽

Hyperbolic Function ◽

Hyperbolic Function Method

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Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics

Computer Physics Communications ◽

10.1016/s0010-4655(00)00168-5 ◽

2001 ◽

Vol 133 (2-3) ◽

pp. 158-164 ◽

Cited By ~ 101

Author(s):

Yi-Tian Gao ◽

Bo Tian

Keyword(s):

Nonlinear Equations ◽

Symbolic Computation ◽

Function Method ◽

Mathematical Physics ◽

Hyperbolic Function ◽

Equations Of Mathematical Physics ◽

Hyperbolic Function Method

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Improved hyperbolic function method and exact solutions for variable coefficient Benjamin-Bona-Mahony-Burgers equation

Thermal Science ◽

10.2298/tsci1504183m ◽

2015 ◽

Vol 19 (4) ◽

pp. 1183-1187

Author(s):

Hong-Cai Ma ◽

Xiao-Fang Peng ◽

Dan-Dan Yao

Keyword(s):

Fluid Mechanics ◽

Exact Solutions ◽

Variable Coefficient ◽

Function Method ◽

Burgers Equation ◽

Periodic Wave ◽

Hyperbolic Function ◽

Hyperbolic Function Method

By using the improved hyperbolic function method, we investigate the variable coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.

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Extended Generalized Hyperbolic-function Method and New Exact Solutions of the Generalized Hamiltonian and NNV Equations by the Symbolic Computation

Fundamenta Informaticae ◽

10.3233/fi-2014-1056 ◽

2014 ◽

Vol 132 (4) ◽

pp. 501-517 ◽

Cited By ~ 1

Author(s):

Jian-Guo Liu ◽

Zhi-Fang Zeng

Keyword(s):

Exact Solutions ◽

Symbolic Computation ◽

Function Method ◽

Hyperbolic Function ◽

New Exact Solutions ◽

Hyperbolic Function Method

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New Mathematical Analysis for Nonlinear Simultaneous Differential Equation in Micro-Disk Biosensor Using Hyperbolic Function Method

Journal of Electroanalytical Chemistry ◽

10.1016/j.jelechem.2020.114827 ◽

2020 ◽

pp. 114827

Author(s):

A. Eswari ◽

S. Saravanakumar

Keyword(s):

Differential Equation ◽

Mathematical Analysis ◽

Function Method ◽

Hyperbolic Function ◽

Hyperbolic Function Method ◽

Simultaneous Differential Equation

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Approximate symmetry and solutions of the nonlinear Klein–Gordon equation with a small parameter

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817500463 ◽

2017 ◽

Vol 14 (03) ◽

pp. 1750046

Author(s):

Mohammad Rahimian ◽

Megerdich Toomanian ◽

Mehdi Nadjafikhah

Keyword(s):

Small Parameter ◽

Analytical Solutions ◽

Function Method ◽

Gordon Equation ◽

Hyperbolic Function ◽

Approximate Symmetry ◽

Nonlinear Phenomena ◽

Hyperbolic Function Method ◽

Klein Gordon ◽

Klein Gordon Equation

In this paper, the Lie approximate symmetry analysis is applied to investigate new solutions of the nonlinear Klein–Gordon equation with a small parameter. The nonlinear Klein–Gordon equation is used to model many nonlinear phenomena. The hyperbolic function method and Riccati equation method are employed to solve some of the obtained reduced ordinary differential equations. We construct new analytical solutions with a small parameter which is effectively obtained by the proposed method.

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