Understanding the Non-Relativistic Behavior of the Chern–Simons–Higgs System

In this paper, we consider a singular limit of the Chern–Simons–Higgs equations that reveals a correspondence between the Chern–Simons–Higgs and Chern–Simons–Schrödinger systems. Specifically, we demonstrate that in the limit as the speed of light goes infinity, known as the non-relativistic limit, a family of time-dependent solutions of the modulated Chern–Simons–Higgs system, which depends on the parameter c representing the speed of light, converges to the solution of the Chern–Simons–Schrödinger system, given suitable initial data assumptions.