scholarly journals Nongauge bright soliton of the nonlinear Schrödinger (NLS) equation and a family of generalized NLS equations

2016 ◽  
Vol 31 (03) ◽  
pp. 1650020 ◽  
Author(s):  
M. A. Reyes ◽  
D. Gutiérrez-Ruiz ◽  
S. C. Mancas ◽  
H. C. Rosu
Keyword(s):  
Nonlinear Equations ◽  
Soliton Solution ◽  
Bright Soliton ◽  
Nls Equation ◽  
Potential Term ◽  
Nonlinear Schrödinger ◽  
Bright Soliton Solution ◽  
De Vries ◽  
Constant Potential

We present an approach to the bright soliton solution of the nonlinear Schrödinger (NLS) equation from the standpoint of introducing a constant potential term in the equation. We discuss a “nongauge” bright soliton for which both the envelope and the phase depend only on the traveling variable. We also construct a family of generalized NLS equations with solitonic [Formula: see text] solutions in the traveling variable and find an exact equivalence with other nonlinear equations, such as the Korteveg–de Vries (KdV) and Benjamin–Bona–Mahony (BBM) equations when [Formula: see text].

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.

scholarly journals The soliton solution of a modified nonlinear schrödinger equation

2017 ◽  
Vol 5 (1) ◽  
pp. 16
Author(s):  
Jumei Zhang ◽  
Li Yin
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Equations ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Method ◽  
Hirota Bilinear

Hirota bilinear derivative method can be used to construct the soliton solutions for nonlinear equations. In this paper we construct the soliton solutions of a modified nonlinear Schrödinger equation by bilinear derivative method.

DETERMINANT REPRESENTATION OF N-TIMES DARBOUX TRANSFORMATION FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION

2013 ◽  
Vol 27 (29) ◽  
pp. 1350216 ◽  
Author(s):  
JINGWEI HAN ◽  
JING YU ◽  
JINGSONG HE
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Determinant Representation

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz–Kaup–Newell–Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.

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 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 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.

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