**1. Introduction**

Using electromagnetic wave propagation theory, light transmitting through space is a field problem governed by the well-known nonlinear Schrödinger (NLS) equation. Transmission characteristics, such as redshift, can be deduced from the solution of this NLS equation instead of space expansion, like in the Big Bang, or by energy losses, such as in "tired light" theory. Until recently, the NLS equation has not been solved under conditions appropriate for space. The NLS equation involves two system parameters: a constant coefficient for the linear dispersion term and another constant for the nonlinear self-phase focusing term. As space is sparsely populated with matter, both these constants are extremely small in value. On the other hand, light transitions through space could involve distances of thousands of light years. Chen in 2020 and 2022 has overcome these numerical difficulties in dealing with extremely small and large numbers and developed a numerical method that provides stable soliton solutions that have particle-like characteristics. Solitons can survive the long journey to

reach us notwithstanding what could be encountered on the way. After reviewing those numerical solutions, it is clear that any wavelength changes in the propagation of light are linearly proportional to distance traveled. This fact has been observed by astronomers for many years. However, the change in wavelength is solely due to the innate nature of propagation of electromagnetic waves in a medium.
