https://doi.org/10.1140/epjp/s13360-022-02558-1
Regular Article
Nonlinear corrections to the longitudinal structure function 
from the parametrization of 
: Laplace transform approach
Department of Physics, Razi University, 67149, Kermanshah, Iran
a grboroun@gmail.com, boroun@razi.ac.ir
Received:
17
November
2021
Accepted:
3
March
2022
Published online:
19
March
2022
The nonlinear corrections to the longitudinal structure function is derived at low values of the Bjorken variable x by using the Laplace transforms technique. The nonlinear behavior of the longitudinal structure function is determined with respect to the Gribov–Levin–Ryskin–Mueller–Qiu and Altarelli–Martinelli equations. These results show that the nonlinear longitudinal structure function can be determined directly in terms of the parametrization of 
and the derivative of the proton structure function with respect to 
. These corrections improve the behavior of the longitudinal structure function at low values of 
in comparison with other parametrization methods.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
