Addendum: Susanto, H.; Karjanto, N.; Zulkarnain; Nusantara, T.; Widjanarko, T. Soliton and Breather Splitting on Star Graphs from Tricrystal Josephson Junctions. Symmetry 2019, 11, 271

The authors would like to make the following addenda and correction to their paper [1].

Affiliation

The name of institution was missing from affiliation No. 4. It should be “Department of Mathematics, Faculty of Mathematics and Natural Sciences, Malang State University, Jalan Semarang 5, Malang 65145, Indonesia; [email protected]”.

Scattering in the Linear Problem of the NLS Solitons

In Subsection 3.1 on the scattering in the linear problem of the nonlinear Schrödinger (NLS) solitons, we wrote the following statement:

“It turns out that these coefficients do not satisfy the standard (unitarity) condition due to the following:

$$|\tilde{r}{|}^2+{\left|\tilde{t}\right|}^2=\frac{5}{9}<1,\tilde{t}<1+\tilde{r}=\frac{4}{3}.$$

This informs us that the vertex conditions will not preserve the `mass’ of localized solutions $\mathcal{M}={\int }_{X\in \mathbb{R}}{\left|U\right|}^{2}dX$”.

We would like to clarify the aforementioned statement by adding the following sentences:

“However, referring to the original NLS Equation (5) and its boundary Condition (6), these coefficients satisfy the standard (unitarity) condition due to the following:

$$|\tilde{r}{|}^2+2{\left|\tilde{t}\right|}^2=1,2\tilde{t}=1+\tilde{r}=\frac{4}{3}.$$

Note that there is a factor of 2 because there are two transmitting branches. This informs us that the vertex conditions will preserve the localized solution mass $\mathcal{M}={\int }_{X\in \mathbb{R}}{\left|U\right|}^{2}dX$ in the original model”.