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 Exact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qi Li ◽  
Qiu-yuan Duan ◽  
Jian-bing Zhang
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Soliton Interactions ◽  
Nonlinear Schrödinger ◽  
Multisoliton Solutions

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota’s approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

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].

VARIATIONAL APPROACH TO THE BRIGHT-SOLITON OF THE FOURTH ORDER NONLINEAR SCHRÖDINGER EQUATION WITH CUBIC NONLINEARITY

2012 ◽  
Vol 26 (26) ◽  
pp. 1250147 ◽  
Author(s):  
WEI-MIN ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Fourth Order ◽  
Schrodinger Equation ◽  
Variational Principles ◽  
Nonlinear Schrodinger Equation ◽  
Bright Soliton ◽  
Cubic Nonlinearity ◽  
Nonlinear Schrödinger ◽  
Bright Soliton Solution

Via He's semi-inverse method, variational principles are established for the fourth order nonlinear Schrödinger equation with cubic nonlinearity. Based on the obtained variational formulations, a bright-soliton solution can be obtained using He's variational method.

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