H. Huh and D.E. Pelinovsky
Nonexistence of self-similar blowup for the
nonlinear Dirac equations in (1+1) dimensions
Applied Mathematics Letters 92, 176-183 (2019)
Abstract:
We address a general system of nonlinear Dirac equations in (1+1) dimensions and
prove nonexistence of classical self-similar blowup solutions in the space of bounded functions.
While this argument does not exclude the possibility of finite-time blowup, it still suggests
that smooth solutions to the nonlinear Dirac equations in (1+1) dimensions do not develop
self-similar singularities in a finite time. In the particular case of the cubic Dirac equations,
we characterize (unbounded) self-similar solutions in the closed analytical form.
Keywords:
nonlinear Dirac equations, global existence, finite-time blowup, self-similar solutions