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 - 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 -