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Title: Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)]

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:
 [1] ;  [2] ;  [3] ;  [4] ;  [5]
  1. Univ. of Bayreuth (Germany). Inst. of Physics
  2. Univ. of Seville (Spain). Dept. of Applied Physics. IMUS
  3. 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
  4. Indian Inst. of Science Education and Research, Pune (India)
  5. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division. Center for Nonlinear Studies
Publication Date:
Report Number(s):
LA-UR-16-20641
Journal ID: ISSN 2470-0045
Grant/Contract Number:
AC52-06NA25396; FIS2014-54497-P
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)
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 Orgs:
Indian Inst. of Science Education and Research, Pune (India); Santa Fe Inst. (SFI), Santa Fe, NM (United States)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
OSTI Identifier:
1338759
Alternate Identifier(s):
OSTI ID: 1252380