Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]
Abstract
In Sec. IV of our original paper, we assumed a particular conservation law Eq. (4.6), which was true in the absence of external potentials, to derive some particular potentials for which we obtained solutions to the nonlinear Dirac equation (NLDE). Because the conservation law of Eq. (4.6) for the component T11 of the energy-momentum tensor is not true in the presence of these external potentials, the solutions we found do not satisfy the NLDEs in the presence of these potentials. Thus all the equations from Eq. (4.6) through Eq. (4.44) are not correct, since the exact solutions that followed in that section presumed Eq. (4.6) was true. Also Eqs. (A3)–(A5) are a restatement of Eq. (4.6) and also are not correct. These latter equations are also not used in Sec. V and beyond. The rest of our original paper (starting with Sec. V) was not concerned with exact solutions, rather it was concerned with how the exact solitary-wave solutions to the NLDE in the absence of an external potential responded to being in the presence of various external potentials. This Erratum corrects this mistake.
- Authors:
-
- Univ. of Bayreuth (Germany). Inst. of Physics
- Univ. of Seville (Spain). Dept. of Applied Physics. IMUS
- Santa Fe Inst. (SFI), Santa Fe, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division. Center for Nonlinear Studies
- Indian Inst. of Science Education and Research, Pune (India)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division. Center for Nonlinear Studies
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Seville (Spain); Univ. of Bayreuth (Germany)
- Sponsoring Org.:
- USDOE; Univ. of Seville (Spain); Regional Government of Andalusia (Spain); Humboldt Foundation (Germany); Ministry of Economy, Industry and Competitiveness (MINECO) (Spain)
- Contributing Org.:
- Indian Inst. of Science Education and Research, Pune (India); Santa Fe Inst. (SFI), Santa Fe, NM (United States)
- OSTI Identifier:
- 1338759
- Alternate Identifier(s):
- OSTI ID: 1252380
- Report Number(s):
- LA-UR-16-20641
Journal ID: ISSN 2470-0045
- Grant/Contract Number:
- AC52-06NA25396; FIS2014-54497-P
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
Citation Formats
Mertens, Franz G., Quintero, Niurka R., Cooper, Fred, Khare, Avinash, and Saxena, Avadh. Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]. United States: N. p., 2016.
Web. doi:10.1103/PhysRevE.93.059903.
Mertens, Franz G., Quintero, Niurka R., Cooper, Fred, Khare, Avinash, & Saxena, Avadh. Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]. United States. https://doi.org/10.1103/PhysRevE.93.059903
Mertens, Franz G., Quintero, Niurka R., Cooper, Fred, Khare, Avinash, and Saxena, Avadh. Tue .
"Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]". United States. https://doi.org/10.1103/PhysRevE.93.059903. https://www.osti.gov/servlets/purl/1338759.
@article{osti_1338759,
title = {Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]},
author = {Mertens, Franz G. and Quintero, Niurka R. and Cooper, Fred and Khare, Avinash and Saxena, Avadh},
abstractNote = {In Sec. IV of our original paper, we assumed a particular conservation law Eq. (4.6), which was true in the absence of external potentials, to derive some particular potentials for which we obtained solutions to the nonlinear Dirac equation (NLDE). Because the conservation law of Eq. (4.6) for the component T11 of the energy-momentum tensor is not true in the presence of these external potentials, the solutions we found do not satisfy the NLDEs in the presence of these potentials. Thus all the equations from Eq. (4.6) through Eq. (4.44) are not correct, since the exact solutions that followed in that section presumed Eq. (4.6) was true. Also Eqs. (A3)–(A5) are a restatement of Eq. (4.6) and also are not correct. These latter equations are also not used in Sec. V and beyond. The rest of our original paper (starting with Sec. V) was not concerned with exact solutions, rather it was concerned with how the exact solitary-wave solutions to the NLDE in the absence of an external potential responded to being in the presence of various external potentials. This Erratum corrects this mistake.},
doi = {10.1103/PhysRevE.93.059903},
journal = {Physical Review E},
number = 5,
volume = 93,
place = {United States},
year = {Tue May 10 00:00:00 EDT 2016},
month = {Tue May 10 00:00:00 EDT 2016}
}
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