Ground States and Bound States of a Nonlinear Schrödinger System

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Zhaoli Liu ◽  
Zhi-Qiang Wang
Keyword(s):  
Bound States ◽  
Ground States ◽  
Nonlinear Schrödinger ◽  
Existence And Multiplicity ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

AbstractThis paper concerns existence and multiplicity of ground states and bound states of the time-independent Schrödinger systemwhere n = 2, 3, N ≥ 2, λand β

Vector Dark Solitons for a Coupled Nonlinear Schrödinger System with Variable Coefficients in an Inhomogeneous Optical Fibre

2017 ◽  
Vol 72 (8) ◽  
pp. 779-787 ◽  
Author(s):  
Lei Liu ◽  
Bo Tian ◽  
Xiao-Yu Wu ◽  
Yu-Qiang Yuan
Keyword(s):  
Optical Fibre ◽  
Bound States ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Variable Coefficients ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

AbstractStudied in this paper are the vector dark solitons for a coupled nonlinear Schrödinger system with variable coefficients, which can be used to describe the pulse simultaneous propagation of the M-field components in an inhomogeneous optical fibre, where M is a positive integer. When M=2, under the integrable constraint, we construct the nondegenerate N-dark-dark soliton solutions in terms of the Gramian through the Kadomtsev–Petviashvili hierarchy reduction. With the help of analytic analysis, a vector one soliton with varying amplitude and velocity is studied. Interactions and bound states between the two solitons under different group velocity dispersion and amplification/absorption coefficients are presented. Moreover, we extend our analysis to any M to obtain the nondegenerate vector N-dark soliton solutions.

scholarly journals Ground States for a Nonlinear Schrödinger System with Sublinear Coupling Terms

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Filipe Oliveira ◽  
Hugo Tavares
Keyword(s):  
Ground States ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrödinger System ◽  
Coupling Terms ◽  
Schrödinger System

AbstractWe study the existence of ground states for the coupled Schrödinger system

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