scholarly journals Bidirectional solitary wave solutions and soliton solutions for two nonlinear ev olution equations

2003 ◽  
Vol 52 (8) ◽  
pp. 1848
Author(s):  
Xu Gui-Qiong ◽  
Li Zhi-Bin
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions

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.

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.

scholarly journals On the wave solutions to the TRLW equation

2018 ◽  
Vol 22 ◽  
pp. 01033
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Canan Unlu ◽  
Hasan Bulut
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Models ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
2D And 3D ◽  
Singular Soliton

In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science.

A Variety of Exact Periodic Wave and Solitary Wave Solutions for the Coupled Higgs Equation

2012 ◽  
Vol 67 (10-11) ◽  
pp. 545-549 ◽  
Author(s):  
Houria Trikia ◽  
Abdul-Majid Wazwazb
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Higgs Field ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Jacobi Elliptic Function ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Jacobi Elliptic Function Expansion

In this work, the coupled Higgs field equation is studied. The extended Jacobi elliptic function expansion methods are efficiently employed to construct the exact periodic solutions of this model. As a result, many exact travelling wave solutions are obtained which include new shock wave solutions or kink-shaped soliton solutions, solitary wave solutions or bell-shaped soliton solutions, and combined solitary wave solutions are formally obtained.

Soliton Solutions for Some Nonlinear Partial Differential Equations in Mathematical Physics Using He’s Variational Method

2020 ◽  
Vol 21 (2) ◽  
pp. 147-158 ◽  
Author(s):  
Mohammed K. Elboree
Keyword(s):  
Solitary Wave ◽  
Inverse Method ◽  
Variational Principles ◽  
Ritz Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Solitary Wave Solutions ◽  
Kp Equation ◽  
Wave Solutions

AbstractIn this paper, we constructed the variational principles for Bogoyavlensky–Konopelchenko equation, the generalized (3+1)-dimensional nonlinear wave in liquid containing gas bubbles and a new coupled Kadomtsev–Petviashvili (KP) equation via He’s semi-inverse method. Based on this formulation, we obtained the solitary wave solutions via Ritz method. We explained the properties of the soliton waves numerically by some figures. Finally, the physical interpretation for these solutions are obtained.

EXACT SOLITON SOLUTIONS FOR THE HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 16 (08) ◽  
pp. 1225-1237 ◽  
Author(s):  
BIAO LI
Keyword(s):  
Solitary Wave ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Higher Order ◽  
Solitary Wave Solutions ◽  
Ansatz Method ◽  
Complex Envelope ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Special Cases

Based on the complex envelope ansatz method, the projective Riccati equation method and q-deformed hyperbolic functions, a method is developed for constructing a series of exact analytical solutions for higher-order nonlinear Schrödinger (HNLS) equation, which describes propagation of femtosecond light pulse in optical fiber under certain parametric conditions. With the help of symbolic computation, six families of new solitary wave solutions are obtained. The solitary wave solutions obtained by Li et al.18 are special cases of our solutions. The novel soliton solutions can describe W-shaped, bright and dark soliton properties in the same expression and their amplitude may approach nonzero when the time variable approaches infinity. Furthermore, the soliton propagation and solitons interaction scenario are discussed and simulated by computer.

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