**Abstract**

Problems related to Big Bang because of the Doppler interpretation of cosmological redshift have not been resolved up to recent years. The "tired light" theory proposes an energy loss model that has its own limitations. Chen in 2020 and 2021 proposed to treat light propagation through the space just as a field problem involving electromagnetic waves and governed by the well-known nonlinear Schrödinger (NLS) equation. The space is not a vacuum and is sparsely populated with matters. Electromagnetic waves traveling through the space will undergo changes as predicted by the NLS equation involving a linear dispersion and a nonlinear self-phase focusing terms. Using the cosmological principle, the coefficients associated with these terms could be constants but extremely small in value. Special numerical methods have been developed and could be used to find both bright and dark soliton-like solutions for the NLS equation that are stable and could travel through the extremely long distance involved. These solutions clearly show the redshift is linearly proportional to distance traveled for both bright and dark solitons. The conclusion is that redshift (and blue shift) is an innate nature of light traveling through the space.

**Keywords:** wave propagation, nonlinear Schrödinger equation, tired light, big bang, cosmological redshift, Hubble's law
