Soliton and Breather Splitting on Star Graphs from Tricrystal Josephson Junctions
Round 1
Reviewer 1 Report
The paper needs major clarifications and rewriting. Please see my Review for more details.
Comments for author File: 
Comments.pdf
Author Response
Please see the attached file.
Author Response File: Author Response.pdf
Reviewer 2 Report
In the broader and timely context of the experimental, numerical and
theoretical study of various physical systems living on graphs the
authors restricted their attention to the first nontrivial tri-star
graph of Figure 1. They decided to analyze and discuss the dynamics
of non-topological solitons in such a kinematical setting.
The novelty of this study is twofold. Firstly, the motion of the
system in question is assumed controlled by the sine-Gordon (sG)
equation while, secondly, an interesting mathematical concept is
introduced in an attempted reduction of the model into its nonlinear
Schr\"{o}dinger (NLS) analogue.
The methods used are mainly numerical. Typically, the NLS soliton
scattering is treated via an integration of the NLS equation by
means of the conventional Runge-Kutta fourth-order method. The
discretization (using a three-point central difference) is also
routine - in the context of a more ambitious numerical mathematics
one would appreciate seeing at least some comments on the possible
role of the propagation of round-off errors.
On a more general level the authors have shown that the sG -> NLS
transformation can only be well formulated in the arrangement using
the small-amplitude breather solutions in the original setting. In
such a case (characterized, remarkably, up to the approximations
made, by another soliton dynamics) it is pointed out that an ad hoc
modification of the matching conditions at the vertex is necessary.
The results of this paper are also phenomenologically relevant.
Related, in the language of simulations and possible experimental
realizations, to the Josephson junctions. Nevertheless, putting
these terms in the title of the paper can be found slightly
misleading because the essence of the message is , predominantly,
numerical. Illustrated, i.a., by the carefully selected pictures.
Naturally, this can be viewed, after all, just as the acceptable
choice of the strategy of the presentation as made by the authors.
Author Response
Please see the attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Dear Authors:
I have reviewed the submitted revised manuscript and am now satisfied by the improvements and corrections that you have made following my suggestions. The paper has been considerably improved and constitutes a new and interesting piece of work in this field.
