Higher-order spectral filtering effects on the dynamics of stationary soliton in dissipative systems in the presence of linear and nonlinear gain/loss

2021 ◽  
Author(s):  
Gaétan Kuetche Saadeu ◽  
Laurent Nana
Keyword(s):  
Higher Order ◽  
Dissipative Systems ◽  
Spectral Filtering ◽  
Nonlinear Gain ◽  
Linear And Nonlinear ◽  
Gain Loss

Chirped Wave Solutions of a Generalized (3+1)-Dimensional Nonlinear Schr¨odinger Equation

2011 ◽  
Vol 66 (6-7) ◽  
pp. 392-400 ◽  
Author(s):  
Xian-Jing Lai ◽  
Xiao-Ou Cai
Keyword(s):  
Dispersion Coefficient ◽  
Periodic Wave ◽  
Variable Coefficients ◽  
Nonlinearity Coefficient ◽  
Nonlinear Gain ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Self Similar ◽  
Linear And Nonlinear ◽  
Gain Loss

The exact chirped soliton-like and quasi-periodic wave solutions of the (3+1)-dimensional generalized nonlinear Schrödinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in this paper. The form and the behaviour of solutions are strongly affected by the modulation of both the dispersion coefficient and the nonlinearity coefficient. In addition, self-similar soliton-like waves precisely piloted from our obtained solutions by tailoring the dispersion and linear gain (loss)

scholarly journals Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120171 ◽  
Author(s):  
M. Duanmu ◽  
K. Li ◽  
R. L. Horne ◽  
P. G. Kevrekidis ◽  
N. Whitaker
Keyword(s):  
Systems Analysis ◽  
Recent Progress ◽  
Dynamical Evolution ◽  
Direct Numerical Simulations ◽  
Nonlinear Gain ◽  
Dynamical Systems Analysis ◽  
Different Types ◽  
Linear And Nonlinear ◽  
Gain Loss ◽  
Asymmetric Solution

In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time ( ) symmetry, i.e. with a spatially odd gain–loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear -symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear -symmetric trimers, while both of them are absent in linear -symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear -symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of -symmetric quadrimers.

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