TY - JOUR
T1 - Families of Localized and Oscillatory Solutions to the Coupled-Nonlinear Two-Dimensional Dirac Equations
AU - Chaachoua Sameut, H.
AU - Asad-uz-zaman, M.
AU - Al Khawaja, U.
AU - Benarous, M.
N1 - Funding Information:
The authors HCS and MB acknowledge the support provided by Hassiba Benbouali University of Chlef, Algeria. The authors MA and UAK acknowledge the support of King Fahd University of Petroleum and Minerals under research group project RG1503-1 and RG1503-2. U. Al Khawaja acknowledges the support of grants UAEU-UPAR(4) 2016 and UAEU UPAR(6) 2017.
Publisher Copyright:
© 2018, Allerton Press, Inc.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - We numerically solve the coupled-nonlinear two-dimensional Dirac equations that describe a virtual spin-1/2 system with cubic nonlinearity.We find that this set of equations supports only oscillatory solutions in the non-relativistic limit and families of discrete localized solutions in the relativistic limit. Each family of the localized solutions is characterized by a constant central amplitude value. Each solution within a family is characterized by a number of nodes and a discrete energy eigenvalue, which is bounded by the rest mass of the particle. We study the effect of different parameters on the localized solutions.
AB - We numerically solve the coupled-nonlinear two-dimensional Dirac equations that describe a virtual spin-1/2 system with cubic nonlinearity.We find that this set of equations supports only oscillatory solutions in the non-relativistic limit and families of discrete localized solutions in the relativistic limit. Each family of the localized solutions is characterized by a constant central amplitude value. Each solution within a family is characterized by a number of nodes and a discrete energy eigenvalue, which is bounded by the rest mass of the particle. We study the effect of different parameters on the localized solutions.
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U2 - 10.3103/S1541308X1804009X
DO - 10.3103/S1541308X1804009X
M3 - Article
AN - SCOPUS:85058787749
SN - 1541-308X
VL - 26
SP - 306
EP - 311
JO - Physics of Wave Phenomena
JF - Physics of Wave Phenomena
IS - 4
ER -