Next Article in Journal
Total Variation Based Neural Network Regression for Nonuniformity Correction of Infrared Images
Next Article in Special Issue
Vortex Creation without Stirring in Coupled Ring Resonators with Gain and Loss
Previous Article in Journal
Force Loading Tracking Control of an Electro-Hydraulic Actuator Based on a Nonlinear Adaptive Fuzzy Backstepping Control Scheme
Previous Article in Special Issue
Spontaneous Symmetry Breaking and Higgs Mode: Comparing Gross-Pitaevskii and Nonlinear Klein-Gordon Equations
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Symmetry 2018, 10(5), 156;

Symmetry Breakings in Dual-Core Systems with Double-Spot Localization of Nonlinearity

Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, Lojasiewicza 11, PL-30-348 Krakow, Poland
Advanced Institute for Science and Technology, Hanoi University of Science and Technology, 100803 Hanoi, Vietnam
Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL-02-093 Warszawa, Poland
Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 29 April 2018 / Revised: 10 May 2018 / Accepted: 10 May 2018 / Published: 13 May 2018
(This article belongs to the Special Issue Broken Symmetry)
Full-Text   |   PDF [1584 KB, uploaded 13 May 2018]   |  


We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two-dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries. View Full-Text
Keywords: self-trapping; soliton; bifurcation; waveguide; parity; asymmetry; stability self-trapping; soliton; bifurcation; waveguide; parity; asymmetry; stability

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Zegadlo, K.B.; Hung, N.V.; Ramaniuk, A.; Trippenbach, M.; Malomed, B.A. Symmetry Breakings in Dual-Core Systems with Double-Spot Localization of Nonlinearity. Symmetry 2018, 10, 156.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top