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.

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

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.

Construction of optical soliton solutions of the generalized nonlinear Radhakrishnan–Kundu–Lakshmanan dynamical equation with power law nonlinearity

2020 ◽  
Vol 34 (13) ◽  
pp. 2050139 ◽  
Author(s):  
Aly R. Seadawy ◽  
Sultan Z. Alamri ◽  
Haya M. Al-Sharari
Keyword(s):  
Optical Fibers ◽  
Dynamical Equation ◽  
Physical Phenomenon ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Solitary Wave Solutions ◽  
Light Pulses ◽  
Wave Solutions ◽  
Different Types ◽  
Modified Simple Equation Method

The propagation of soliton through optical fibers has been studied by using nonlinear Schrödinger’s equation (NLSE). There are different types of NLSEs that study this physical phenomenon such as (GRKLE) generalized Radhakrishnan–Kundu–Lakshmanan equation. The generalized nonlinear RKL dynamical equation, which presents description of the dynamical of light pulses, has been studied. We used two formulas of the modified simple equation method to construct the optical soliton solutions of this model. The obtained solutions can be represented as bistable bright, dark, periodic solitary wave solutions.

SPATIAL SOLITARY WAVES IN GENERALIZED NON-LOCAL NONLINEAR MEDIA

2010 ◽  
Vol 19 (02) ◽  
pp. 311-317 ◽  
Author(s):  
WEI-PING ZHONG ◽  
ZHENG-PING YANG
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Cylindrical Coordinates ◽  
Intensity Pattern ◽  
Nonlinear Media ◽  
Wave Solutions ◽  
Non Local

We introduce a very general self-trapped beam solution to the generalized non-local nonlinear Schrödinger equation in cylindrical coordinates, by combining superpositions of the known single accessible soliton solutions. Specific values of soliton parameters are selected as initial conditions and superpositions of the single soliton solutions in the highly non-local regime are launched into the non-local nonlinear medium with Gaussian response function, to obtain novel numerical solitary wave solutions. Novel solitary waves have been constructed that exhibit unique features whose intensity pattern is formed by various figures.

SOLITARY TRANSMISSION OF NEURONAL SIGNALS APPROACHED VIA HE'S SEMI INVERSE METHOD

2021 ◽  
pp. 48-50
Author(s):  
Ancemma Joseph
Keyword(s):  
Inverse Method ◽  
Signal Transmission ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Solitary Wave Solutions ◽  
Mechanical Wave ◽  
Wave Solutions ◽  
Neuronal Signal ◽  
Nerve Pulse

An investigation of neuronal signal transmission is intended in this paper through the establishment of solitary wave solutions for the improved Heimburg Jackson model governing the propagation of the mechanical wave in biomembranes. The computation of soliton solutions is carried out employing He's semi inverse variational principle. The role of nonlinearity and dispersive effects in the solitonic propation is correlated to the role of compressibility, elasticity, and inertia over the neuronal signal transmission in the unilamellar DPPC vesicles at T = 45o. The study reveals that He's semi inverse method is a direct and effective algebraic method to study the experimental features of the nerve pulse in the biomembranes.

scholarly journals Different Kinds of Singular and Nonsingular Exact Traveling Wave Solutions of the Kudryashov-Sinelshchikov Equation in the Special Parametric Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Can Chen ◽  
Weiguo Rui ◽  
Yao Long
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Dynamic Behaviors ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

In this paper, by using the integral bifurcation method, we studied the Kudryashov-Sinelshchikov equation. In the special parametric conditions, some singular and nonsingular exact traveling wave solutions, such as periodic cusp-wave solutions, periodic loop-wave solutions, smooth loop-soliton solutions, smooth solitary wave solutions, periodic double wave solutions, periodic compacton solutions, and nonsmooth peakon solutions are obtained. Further more, the dynamic behaviors of these exact traveling wave solutions are investigated. It is found that the waveforms of some traveling wave solutions vary with the changes of parameters.

Exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method

1986 ◽  
Vol 19 (5) ◽  
pp. 607-628 ◽  
Author(s):  
W Hereman ◽  
P P Banerjee ◽  
A Korpel ◽  
G Assanto ◽  
A van Immerzeele ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Wave Equations ◽  
Nonlinear Evolution ◽  
Algebraic Method ◽  
Solitary Wave Solutions ◽  
Wave Solutions

Numerical soliton solutions of fractional modied (2 + 1)-dimensional Konopelchenko-Dubrovsky equations in plasma physics

2021 ◽  
Author(s):  
Santanu Saha Ray ◽  
B Sagar
Keyword(s):  
Solitary Wave ◽  
Plasma Physics ◽  
Exact Solutions ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Scheme ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Kansa Method

Abstract In this paper, the time-fractional modied (2+1)-dimensional Konopelchenko-Dubrovsky equations have been solved numerically using the Kansa method, in which the multiquadrics used as radial basis function. To achieve this, a numerical scheme based on nite dierenceand Kansa method has been proposed. Also the solitary wave solutions have been obtained by using Kudryashov technique. The computed results are compared with the exact solutions as well as with the soliton solutions obtained by Kudryashov technique to show the accuracy of the proposed method.

scholarly journals Cusped and Smooth Solitons for the Generalized Camassa-Holm Equation on the Nonzero Constant Pedestal

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Dong Li ◽  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Solitary Wave Solutions ◽  
Nonzero Constant ◽  
Wave Solutions ◽  
Holm Equation

We investigate the traveling solitary wave solutions of the generalized Camassa-Holm equationut - uxxt + 3u2ux=2uxuxx + uuxxxon the nonzero constant pedestallimξ→±∞⁡uξ=A. Our procedure shows that the generalized Camassa-Holm equation with nonzero constant boundary has cusped and smooth soliton solutions. Mathematical analysis and numerical simulations are provided for these traveling soliton solutions of the generalized Camassa-Holm equation. Some exact explicit solutions are obtained. We show some graphs to explain our these solutions.

Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions

2019 ◽  
Vol 33 (18) ◽  
pp. 1950210 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Longitudinal Wave ◽  
Electrostatic Potential ◽  
Graphical Representation ◽  
Algebraic Method ◽  
Hyperbolic Function ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this work, we consider the nonlinear longitudinal wave equation (LWE) which involves mathematical physics with dispersal produced by the phenomena of transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod. We use the extended form of two methods, auxiliary equation mapping and direct algebraic method to investigated the families of solitary wave solutions of one-dimensional nonlinear LWE. These new exact and solitary wave solutions are derived in the form of trigonometric function, periodic solitary wave, rational function, and elliptic function, hyperbolic function, bright and dark solitons solutions of the LWE, which represent the electrostatic potential and pressure for LWE and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica program.

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