scholarly journals Some Analytical Solitary Wave Solutions for the Generalized q-Deformed Sinh-Gordon Equation: ∂2θ/∂z∂ξ=αsinhq⁡(βθγ)p-δ

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
H. Eleuch
Keyword(s):  
Solitary Wave ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Physical Systems ◽  
Wave Solutions ◽  
Modeling Physical Systems

We introduce the generalized q-deformed Sinh-Gordon equation and derive analytical soliton solutions for some sets of parameters. This new defined equation could be useful for modeling physical systems with violated symmetries.

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.

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.

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.

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.

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