scholarly journals Vector Solitons of a Coupled Schrödinger System with Variable Coefficients

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Juan Carlos Muñoz Grajales
Keyword(s):  
Numerical Simulations ◽  
Finite Energy ◽  
Variable Coefficients ◽  
Soliton Equations ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

We show the existence of waveforms of finite-energy (vector solitons) for a coupled nonlinear Schrödinger system with inhomogeneous coefficients. Furthermore, some of these solutions are approximated using a Newton-type iteration, combined with a collocation-spectral strategy to discretize the corresponding soliton equations. Some numerical simulations concerned with analysis of a collision of two oncoming vector solitons of the system are also performed.

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 Synchronized and ground-state solutions to a coupled Schrödinger system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohammad Ali Husaini ◽  
Chuangye Liu
Keyword(s):  
Bounded Domain ◽  
Ground State ◽  
Ground State Solutions ◽  
Nonlinear Schrödinger ◽  
Coupled Schrödinger System ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

<p style='text-indent:20px;'>In this paper, we study the following coupled nonlinear Schrödinger system of the form</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\{\begin{array}{l} -\Delta u_i-\kappa_iu_i = g_i(u_i)+\lambda\partial_iF(\vec{u}), \\ \vec{u} = (u_1,u_2,\cdots,u_m), u_i\in D_0^{1,2}(\Omega), \end{array}\right. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>for <inline-formula><tex-math id="M1">\begin{document}$ m = 2,3 $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M2">\begin{document}$ \Omega\subset \mathbb{R}^N $\end{document}</tex-math></inline-formula> is a bounded domain or <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M4">\begin{document}$ N\geq 3 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ F(t_1,t_2\cdots,t_m)\in C^1(\mathbb{R}^m,\mathbb{R}) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M6">\begin{document}$ \kappa_i\in\mathbb{R} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ g_i\in C(\mathbb{R}) \ (i = 1,2,\cdots,m) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$ \lambda&gt;0 $\end{document}</tex-math></inline-formula> is large enough. In this work we mainly focus on the existence of fully nontrivial ground-state solutions and synchronized ground-state solutions under certain conditions.</p>

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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