Existence and stability of discrete solitons in nonlinear Schrödinger lattices with hard potentials

2020 ◽  
Vol 403 ◽  
pp. 132326
Author(s):  
Qing Zhu ◽  
Zhan Zhou ◽  
Lin Wang
Keyword(s):  
Nonlinear Schrödinger ◽  
Existence And Stability ◽  
Discrete Solitons ◽  
Hard Potentials

BRIGHT SOLITONS IN A PARAMETRICALLY DRIVEN DISCRETE NONLINEAR SCHRODINGER EQUATION

2013 ◽  
Vol 22 ◽  
pp. 570-575 ◽  
Author(s):  
O. P. SWAMI ◽  
V. KUMAR ◽  
A. K. NAGAR
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Discrete Nonlinear Schrödinger Equation ◽  
Nonlinear Schrödinger ◽  
Bright Solitons ◽  
Existence And Stability ◽  
Parametric Driving ◽  
Discrete Solitons

In this paper, we consider a parametrically driven discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright discrete solitons admitted by discrete nonlinear Schrödinger equation. We show that a parametric driving can destabilizes onsite bright solitons and stabilizes intersite bright discrete solitons. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results.

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 02 (04) ◽  
pp. 919-962 ◽  
Author(s):  
FRANK MERLE ◽  
PIERRE RAPHAEL
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Finite Time ◽  
Schrodinger Equation ◽  
Blow Up ◽  
Nonlinear Schrodinger Equation ◽  
Specific Class ◽  
Nonlinear Schrödinger ◽  
Existence And Stability

We consider the L2 critical nonlinear Schrödinger equation [Formula: see text] in the energy space H1. In the series of papers [11–15,18], we studied finite time blow up solutions for which lim t↑T < + ∞ |∇ u(t)|L2 = + ∞ and proved classification results of the blow up dynamics for the specific class of small super critical L2 mass initial data. We extend these results here to a wider class of finite time blow up solutions corresponding to the ones which accumulate at one point exactly the ground state mass. In particular, we prove the existence and stability of large L2 mass log-log type solutions which are believed to describe the generic blow up dynamics.

Stability of discrete solitons in nonlinear Schrödinger lattices

2005 ◽  
Vol 212 (1-2) ◽  
pp. 1-19 ◽  
Author(s):  
D.E. Pelinovsky ◽  
P.G. Kevrekidis ◽  
D.J. Frantzeskakis
Keyword(s):  
Nonlinear Schrödinger ◽  
Discrete Solitons
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