scholarly journals Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

AIP Advances ◽  
2014 ◽  
Vol 4 (6) ◽  
pp. 067131 ◽  
Author(s):  
Ying Wang ◽  
Yu Zhou
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Pitaevskii Equation ◽  
Exact Soliton Solutions

New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

2021 ◽  
pp. 2150444
Author(s):  
Loubna Ouahid ◽  
M. A. Abdou ◽  
S. Owyed ◽  
Sachin Kumar
Keyword(s):  
Evolution Equations ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Optical Soliton ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Closed Form Solutions ◽  
Special Solutions ◽  
Engineering Physics ◽  
Exact Soliton Solutions

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods’ performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order.

The Soliton Control Research for the Nonlinear ITO System

2010 ◽  
Vol 29-32 ◽  
pp. 762-767
Author(s):  
Yu Lan Ma ◽  
Bang Qing Li
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Soliton Control ◽  
Control Research ◽  
Exact Soliton Solutions

The exact soliton solutions are constructed by extending the (G'/G)-expansion method for the nonlinear ITO system. The soliton controls are investigated. The soliton shapes can be under the control of the parameters related to the (G'/G)-expansion method.

scholarly journals Optical singular and dark solitons to the nonlinear Schrodinger equation in magneto-optic waveguides with anti-cubic nonlinearity.

2021 ◽  
Author(s):  
Thilagarajah Mathanaranjan ◽  
Hadi Rezazadeh ◽  
Mehmet Senol ◽  
Lanre Akinyemi
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Modified Simple Equation Method ◽  
Exact Soliton Solutions ◽  
Magneto Optic

Abstract The present paper aims to investigate the coupled nonlinear Schrodinger equation (NLSE) in magneto-optic waveguides having anti-cubic (AC) law nonlinearity. The solitons secured to magneto-optic waveguides with AC law nonlinearity are extremely useful to fiber-optic transmission technology. Three constructive techniques, namely, the (G'/G)-expansion method, the modified simple equation method (MSEM), and the extended tanh-function method are utilized to find the exact soliton solutions of this model. Consequently, dark, singular and combined dark-singular soliton solutions are obtained. The behaviours of soliton solutions are presented by 3D and 2D plots.

Exact soliton solutions for the core of dispersion-managed solitons

2003 ◽  
Vol 68 (4) ◽  
Author(s):  
Zhiyong Xu ◽  
Lu Li ◽  
Zhonghao Li ◽  
Guosheng Zhou ◽  
K. Nakkeeran
Keyword(s):  
Soliton Solutions ◽  
The Core ◽  
Exact Soliton Solutions

On the exact soliton solutions and different wave structures to the double dispersive equation

2022 ◽  
Vol 54 (2) ◽  
Author(s):  
Usman Younas ◽  
Muhammad Bilal ◽  
Tukur Abdulkadir Sulaiman ◽  
Jingli Ren ◽  
Abdullahi Yusuf
Keyword(s):  
Soliton Solutions ◽  
Dispersive Equation ◽  
Exact Soliton Solutions

Analytical study of exact solutions of the nonlinear Korteweg–de Vries equation with space–time fractional derivatives

2018 ◽  
Vol 32 (02) ◽  
pp. 1850012 ◽  
Author(s):  
Jiangen Liu ◽  
Yufeng Zhang
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Space Time ◽  
Strong Basis ◽  
De Vries

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg–de Vries equation with space–time local fractional derivatives. By using the improved [Formula: see text]-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

2021 ◽  
pp. 2150263
Author(s):  
A. Tripathy ◽  
S. Sahoo ◽  
S. Saha Ray ◽  
M. A. Abdou
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Ode Method ◽  
Novel Methods

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

2022 ◽  
Author(s):  
Yajie Yang ◽  
Ying Dong
Keyword(s):  
Similarity Transformation ◽  
Soliton Solutions ◽  
Gain Coefficient ◽  
Loss Coefficient ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Loss Parameter ◽  
Dynamical Properties ◽  
Bose Einstein ◽  
Loss Effect

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross-Pitaevskii equation describing the three-component Bose-Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

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