scholarly journals Soliton Solutions of a General Rosenau-Kawahara-RLW Equation

2015 ◽  
Vol 7 (2) ◽  
pp. 24 ◽  
Author(s):  
Jin-ming Zuo
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Conserved Quantities ◽  
Rlw Equation ◽  
Bright Soliton Solution

In this paper, we consider a general Rosenau-Kawahara-RLW equation. The exact bright and dark soliton solutions for the consideredmodel are obtained by sech and tanh ansatzes methods. The mass and momentum conserved quantities are also calculated for the case of bright soliton solution.

scholarly journals Discrete Bright-dark Soliton Interaction Dynamic Behaviors for Nonautonomous 2+1-Dimensional Soliton Equation

2021 ◽  
Author(s):  
Li Li ◽  
fajun yu
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
The Novel ◽  
Optical Fields ◽  
Dynamic Behaviors ◽  
Spatial Part ◽  
Bright Soliton Solution ◽  
Temporal Parts ◽  
Interaction Dynamic

Abstract The non-autonomous discrete bright-dark soliton solutions(NDBDSSs) of the 2+1-dimensional Ablowitz-Ladik(AL) equation are derived. We analyze the dynamic behaviors and interactions of the obtained 2+1-dimensional NDBDSSs. In this paper, we present two kinds of different methods to control the 2+1-dimensional NDBDSSs. In first method, we can only control the wave propagations through the spatial part, since the time function has not effect in the phase part. In second method, we can control the wave propagations through both the spatial and temporal parts. The different propagation phenomena can also be produced through two kinds of managements. We obtain the novel "л"-shape non-autonomous discrete bright soliton solution(NDBSS), the novel "λ"-shape non-autonomous discrete dark soliton solution(NDDSS) and their interaction behaviors. The novel behaviors are considered analytically, which can be applied to the electrical and optical fields.

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRÖDINGER EQUATION

2011 ◽  
Vol 21 (09) ◽  
pp. 2623-2628
Author(s):  
JIANMING ZHANG ◽  
SHUMING LI
Keyword(s):  
Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Generalized Schrödinger Equation ◽  
Bright Soliton Solution

Using the method of dynamical systems for the generalized Schrödinger equation, the bright soliton solution, dark soliton solution, uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. Exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

scholarly journals BRIGHT AND DARK SOLITON SOLUTIONS OF THE (2 + 1)-DIMENSIONAL EVOLUTION EQUATIONS

2014 ◽  
Vol 19 (1) ◽  
pp. 118-126 ◽  
Author(s):  
Ahmet Bekir ◽  
Adem C. Cevikel ◽  
Ozkan Guner ◽  
Sait San
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equations ◽  
Evolution Equations ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Bright Soliton ◽  
Physical Parameters ◽  
Kp Equation ◽  
Constant Coefficients

In this paper, we obtained the 1-soliton solutions of the (2+1)-dimensional Boussinesq equation and the Camassa–Holm–KP equation. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions and another wave ansatz in the form of tanhp function we obtain exact dark soliton solutions for these equations. The physical parameters in the soliton solutions are obtained nonlinear equations with constant coefficients.

scholarly journals Bright soliton solution in 1D Tonks-Girardeau gas

2008 ◽  
Vol 57 (3) ◽  
pp. 1343
Author(s):  
Liu Hong ◽  
Wei Jia-Yu ◽  
Lou Sen-Yue ◽  
He Xian-Tu
Keyword(s):  
Soliton Solution ◽  
Bright Soliton ◽  
Bright Soliton Solution

scholarly journals Some analytical solutions by mapping methods for non-linear conformable time-fractional PHI-4 equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1815-1822 ◽  
Author(s):  
Zeliha Korpinar
Keyword(s):  
Fractional Derivative ◽  
Periodic Solutions ◽  
Soliton Solution ◽  
Analytical Solutions ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Conformable Fractional Derivative ◽  
Singular Soliton

In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-4 equation by means of conformable fractional derivative. The solutions are derived using Jacobi?s elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are iden?tified bright optical soliton, dark soliton, singular soliton, combo soliton solution, and periodic solutions.

scholarly journals Bright Soliton Solution of (1+1)-Dimensional Quantum System with Power-Law Dependent Nonlinearity

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Yukun Zhao ◽  
Yujie Chen ◽  
Jun Dai ◽  
Ying Wang ◽  
Wei Wang
Keyword(s):  
Quantum System ◽  
Power Law ◽  
Soliton Solution ◽  
Expansion Method ◽  
Bright Soliton ◽  
Theoretical Treatment ◽  
Third Order ◽  
Third Order Dispersion ◽  
Bright Soliton Solution ◽  
Order Dispersion

We study the nonlinear dynamics of (1+1)-dimensional quantum system in power-law dependent media based on the nonlinear Schrödinger equation (NLSE) incorporating power-law dependent nonlinearity, linear attenuation, self-steepening terms, and third-order dispersion term. The analytical bright soliton solution of this NLSE is derived via the F-expansion method. The key feature of the bright soliton solution is pictorially demonstrated, which together with typical analytical formulation of the soliton solution shows the applicability of our theoretical treatment.

scholarly journals Multisoliton Solutions and Breathers for the Coupled Nonlinear Schrödinger Equations via the Hirota Method

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Ting-Ting Jia ◽  
Yu-zhen Chai ◽  
Hui-Qin Hao
Keyword(s):  
Soliton Solution ◽  
Bilinear Form ◽  
Schrodinger Equation ◽  
Optical Solitons ◽  
Hirota Method ◽  
Bright Soliton ◽  
Nonlinear Schrödinger ◽  
Bright Soliton Solution ◽  
Multisoliton Solutions ◽  
Better Than

Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations with dissipation terms by the Hirota method, which are better than the formal Schrödinger equation in eliciting optical solitons. The bilinear form has been constructed, via which multisolitons and breathers are derived. In particular, the three-bright soliton solution and breathers are derived and simulated via some pictures. The propagation characters are analysed with the change of the parameters.

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