The Stochastic Schrödinger–Hirota equation plays a crucial role in describing the quantum behavior of physical
systems under the influence of stochastic processes. In this manuscript, we present a comprehensive study on
the exact solutions of the Stochastic Schrödinger–Hirota equation employing a novel approach, namely the
variable coefficient third-degree generalized Abel equation method. This method extends the applicability of
Abel’s equation with variable coefficients, providing a powerful tool for solving complex nonlinear equations
arising in stochastic quantum mechanics. The manuscript findings hold potential implications for diverse
fields, including quantum physics, statistical mechanics, and mathematical physics. Moreover, the developed
methodology could find applications in solving other nonlinear equations arising in different branches of
science and engineering, broadening its scope and impact.