Abstract
We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Stationary soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these solutions provide reflectionless vertex transmission of the Dirac solitons under suitable conditions. The constraints for bond nonlinearity coefficients, conjectured to represent necessary conditions for allowing reflectionless transmission over a Y-junction are derived. The Y-junction considerations are also generalized to a tree and triangle network. The analytical results are confirmed by direct numerical simulations.
Highlights
Nonlinear evolution equations on networks have attracted much attention recently [1,2,3,4,5,6,7,8,9,10]
In this paper we address the problem of the nonlinear Dirac equation on simple metric graphs by focusing on conservation laws and soliton transmission at the graph vertices
A relevant such possibility consists of the discrete waveguide arrays of [43, 48] that can be formulated as a branched system to be described by a nonlinear Dirac equation on metric graphs
Summary
Follow this and additional works at: https://scholarworks.umass.edu/math_faculty_pubs. K K; Babajanov, D B; Matrasulov, D U; and Kevrekidis, P G, "Dynamics of Dirac solitons in networks" (2018). To cite this article: K K Sabirov et al 2018 J. 51 435203 View the article online for updates and enhancements. This content was downloaded from IP address 128.119.169.192 on 15/10/2018 at 15:34. Received 13 June 2018, revised 4 September 2018 Accepted for publication 7 September 2018 Published 26 September 2018
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