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Addendum

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

1
Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, UK
2
Department of Mathematics, University College, Sungkyunkwan University, Natural Science Campus, 2066 Seobu-ro, Jangan-gu, Suwon 16419, Gyeonggi-do, Korea
3
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Kampus Bina Widya KM 12.5, Simpang Baru, Tampan, Kota Pekanbaru, Riau 28293, Indonesia
4
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Malang State University, Jalan Semarang 5, Malang 65145, Indonesia
5
Manufacturing Metrology Team, Faculty of Engineering, The University of Nottingham, Advanced Manufacturing Building, Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1151; https://doi.org/10.3390/sym12071151
Submission received: 11 June 2020 / Accepted: 1 July 2020 / Published: 9 July 2020
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:
| r ˜ | 2 + | t ˜ | 2 = 5 9 < 1 , t ˜ < 1 + r ˜ = 4 3 .
This informs us that the vertex conditions will not preserve the `mass’ of localized solutions M = X R | U | 2 d X ”.
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:
| r ˜ | 2 + 2 | t ˜ | 2 = 1 , 2 t ˜ = 1 + r ˜ = 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 M = X R | U | 2 d X in the original model”.

Funding

The funding information should be corrected as “N.K. was solely funded by the Samsung Intramural Research Fund of Sungkyunkwan University through Grant No. 2016-1299-000”.
The authors would like to apologize for any inconvenience caused to the readers by these changes. The changes do not affect the scientific results. The manuscript will be updated and the original will remain online on the article webpage, with reference to this Addendum.

Conflicts of Interest

The authors declare no conflict of interest.

Reference

  1. Susanto, H.; Karjanto, N.; Zulkarnain; Nusantara, T.; Widjanarko, T. Soliton and Breather Splitting on Star Graphs from Tricrystal Josephson Junctions. Symmetry 2019, 11, 271. [Google Scholar] [CrossRef] [Green Version]

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MDPI and ACS Style

Susanto, H.; Karjanto, N.; Zulkarnain; Nusantara, T.; Widjanarko, T. 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. Symmetry 2020, 12, 1151. https://doi.org/10.3390/sym12071151

AMA Style

Susanto H, Karjanto N, Zulkarnain, Nusantara T, Widjanarko T. 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. Symmetry. 2020; 12(7):1151. https://doi.org/10.3390/sym12071151

Chicago/Turabian Style

Susanto, Hadi, Natanael Karjanto, Zulkarnain, Toto Nusantara, and Taufiq Widjanarko. 2020. "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" Symmetry 12, no. 7: 1151. https://doi.org/10.3390/sym12071151

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